Craig Brown has resigned as manager of Motherwell and is expected to move to the vacant job at Aberdeen.
The 70-year-old had rejected an approach from the Dons' chairman, Stewart Milne, on Wednesday.
But, after a second approach, Brown said he would discuss his options with assistant Archie Knox on Thursday.
"We've not arranged to meet again," said Brown. "But we had a call from Stewart Milne saying that he respected our decision but would we reconsider."
Brown, who was working without a contract at Fir Park, had been adamant that the decision would not be affected by the wages on offer.
Motherwell's ability to retain their squad, or add to it, and proximity to family would come into play and he also said it would be very unlikely that he and Knox would go their separate ways.
"Archie and I haven't had a chance to sit down and consider what he's suggested," said Brown ahead of his decision to resign at Fir Park.
"But we'll do that. At present, we stick to what we said. It would be a big wrench.
"I couldn't give you odds, but we did decide to stay yesterday and it would take quite a massive change of heart for us to alter that."
Brown insisted he was not holding Motherwell to ransom over additional funds for his squad.
"I am not putting a gun at Motherwell's head, but we have three players out of contract in January and, if we thought we weren't able to keep them, it would be quite depressing for us and there is at least one guy we would like to sign," he said.
"We might need one or two assurances, but we know the financial situation and we know there isn't money aplenty to replenish the squad.
"We need a wee bit of understanding that, if we want to push on and improve our position, we need better resources.
"We're looking for some divine inspiration to tell us what to do here. But we respect both clubs greatly and I cannot express my indebtedness to Motherwell enough for giving us this opportunity."
The veteran pair spoke with officials from Aberdeen on Tuesday, but Brown told BBC Scotland the following day that they were not specifically offered the job.
Brown and Knox have firmly established Motherwell in the top six of the Scottish Premier League on a limited budget since taking over in December 2009.
Knox has an Aberdeen connection, having worked with great success as assistant to Sir Alex Ferguson at Pittodrie in the early 1980s.
Aberdeen, who are due to host Motherwell on 18 December, earlier insisted they had not offered Brown the job.
"The situation at present is that we are undertaking due diligence on a limited number of potential candidates, but we are not yet at the stage of making an offer to anyone," said a club statement.
"As has been widely reported, as part of this process, we enquired whether Craig Brown and Archie Knox would be interested in the possibility of coming to Aberdeen and that is as far as it went."
However, asking them to reconsider suggests that former Clyde, Preston and Scotland boss Brown is their number one target.
Motherwell captain Stephen Craigan thought Brown and Knox had done a great job since taking over from Jim Gannon.
"The fact that he is a nice man, is a genuine man, he loves football, I think that's the big thing and its something he has not lost that throughout the years," said the Northern Ireland international.
"I only met Craig a year ago when he joined the club and I think it has shown throughout the year he's had that he enjoys football.
"He has done very well and he knows how to speak to people and how to conduct himself and that is what we have enjoyed."
Commenting on the approach from Aberdeen, Motherwell chief executive Leeann Dempster said on Wednesday: "Given the fantastic on-field success in 2010, it is not surprising that other clubs are taking an interest in our management team.
"With that in mind, we can confirm that representatives from Aberdeen Football Club met briefly with both Craig Brown and Archie Knox yesterday afternoon.
"However, both have decided to reject any approach and reiterated their commitment to Motherwell Football Club. We look forward to continued success under both men in the future."
Scotland Under-21 manager Billy Stark and former Hibernian manager John Hughes were also among the leading contenders.
Former Dons striker Billy Dodds also expressed an interest, while Raith Rovers boss John McGlynn was linked with succeeding the sacked Mark McGhee.
The 70-year-old had rejected an approach from the Dons' chairman, Stewart Milne, on Wednesday.
But, after a second approach, Brown said he would discuss his options with assistant Archie Knox on Thursday.
"We've not arranged to meet again," said Brown. "But we had a call from Stewart Milne saying that he respected our decision but would we reconsider."
Brown, who was working without a contract at Fir Park, had been adamant that the decision would not be affected by the wages on offer.
Motherwell's ability to retain their squad, or add to it, and proximity to family would come into play and he also said it would be very unlikely that he and Knox would go their separate ways.
"Archie and I haven't had a chance to sit down and consider what he's suggested," said Brown ahead of his decision to resign at Fir Park.
"But we'll do that. At present, we stick to what we said. It would be a big wrench.
"I couldn't give you odds, but we did decide to stay yesterday and it would take quite a massive change of heart for us to alter that."
Brown insisted he was not holding Motherwell to ransom over additional funds for his squad.
"I am not putting a gun at Motherwell's head, but we have three players out of contract in January and, if we thought we weren't able to keep them, it would be quite depressing for us and there is at least one guy we would like to sign," he said.
"We might need one or two assurances, but we know the financial situation and we know there isn't money aplenty to replenish the squad.
"We need a wee bit of understanding that, if we want to push on and improve our position, we need better resources.
"We're looking for some divine inspiration to tell us what to do here. But we respect both clubs greatly and I cannot express my indebtedness to Motherwell enough for giving us this opportunity."
The veteran pair spoke with officials from Aberdeen on Tuesday, but Brown told BBC Scotland the following day that they were not specifically offered the job.
Brown and Knox have firmly established Motherwell in the top six of the Scottish Premier League on a limited budget since taking over in December 2009.
Knox has an Aberdeen connection, having worked with great success as assistant to Sir Alex Ferguson at Pittodrie in the early 1980s.
Aberdeen, who are due to host Motherwell on 18 December, earlier insisted they had not offered Brown the job.
"The situation at present is that we are undertaking due diligence on a limited number of potential candidates, but we are not yet at the stage of making an offer to anyone," said a club statement.
"As has been widely reported, as part of this process, we enquired whether Craig Brown and Archie Knox would be interested in the possibility of coming to Aberdeen and that is as far as it went."
However, asking them to reconsider suggests that former Clyde, Preston and Scotland boss Brown is their number one target.
Motherwell captain Stephen Craigan thought Brown and Knox had done a great job since taking over from Jim Gannon.
"The fact that he is a nice man, is a genuine man, he loves football, I think that's the big thing and its something he has not lost that throughout the years," said the Northern Ireland international.
"I only met Craig a year ago when he joined the club and I think it has shown throughout the year he's had that he enjoys football.
"He has done very well and he knows how to speak to people and how to conduct himself and that is what we have enjoyed."
Commenting on the approach from Aberdeen, Motherwell chief executive Leeann Dempster said on Wednesday: "Given the fantastic on-field success in 2010, it is not surprising that other clubs are taking an interest in our management team.
"With that in mind, we can confirm that representatives from Aberdeen Football Club met briefly with both Craig Brown and Archie Knox yesterday afternoon.
"However, both have decided to reject any approach and reiterated their commitment to Motherwell Football Club. We look forward to continued success under both men in the future."
Scotland Under-21 manager Billy Stark and former Hibernian manager John Hughes were also among the leading contenders.
Former Dons striker Billy Dodds also expressed an interest, while Raith Rovers boss John McGlynn was linked with succeeding the sacked Mark McGhee.
