The likes of John Souttar, Andrew Robertson and Stuart Armstrong have been linked with moves to the English Premier League, with Ryan Gauld and Gary Mackay-Steven also attracting interest.
But Thompson will not let any of the players leave Tannadice on the cheap and has warned of the dangers of leaving the club too soon after highlighting the example of Scott Allan.
"No one will leave United this month - not unless a very exceptional offer comes in," said Thompson in the Sunday Mail. "And by exceptional offer, I don't mean any of this £400,000 or £500,000 stuff.
"We don't need to sell. We want to build this team up, not dismantle it. Our aim is that this side will be together for the rest of this season and hopefully into next."
He added: "Some players leave for all the wrong reasons and end up falling into reserve teams.
"The best - or worst - example I can think of in recent times is Scott Allan. Scott was a great player but he hardly kicked a ball when he went to West Brom. His career has gone nowhere in two years.
"Young players such as Gauld, Armstrong, Souttar and Mackay-Steven are better off playing and learning under Jackie McNamara.
"These players will leave eventually, of course they will. What we don't want to do is lose anyone under freedom of contract. Right now, though, we don't need to sell anyone."