Dundee United could sell Gary Mackay-Steven
The Scotland international is out of contract at the end of the campaign and is understood to be keen on a return to English football.
United have tried to get the player to sign a longer deal but have so far failed in their attempts.
“Part of the problem is that he has seen some of the other boys move south and he wants the opportunity to do that,” Thompson said.
“I know Jackie has tried and will continue to try, but you can’t force someone to sign.
“He wants to move to England. That is his ambition and he is 23 now.
“I can understand his point of view, but he has security here and a lot of players who have gone down there have not done particularly well.
“There is a limit to what we can do, but we will do our best to keep him at Tannadice.”
Mackay-Steven moved to Tannadice in the summer of 2011 after a short spell with Aidrie United helped resurrect his football career.
The skilful youngster from Thurso had found himself on the football scrapheap following a series of terrible injury problems with Liverpool and then Fulham.
He immediately impressed with United and has been an ever present in the first team squad, when fit, ever since.
Thompson stressed that the club are not ready to give up the battle, but conceded they may have to think about a January sale if a new deal cannot be agreed in the meantime.
“I am not interested in selling anybody else in this window and I would like to get Gary on a longer contract,” Thompson continued.
“Things might change in January because he is out of contract and we have to look after the club.
“If he hasn’t signed a new deal and you get an offer then we would have to weigh it up.”