Celtic were linked with the 21-year-old full-back before and the Tannadice chief has now reported that the two Championship sides have joined the hunt.
Thompson said in the Scottish Daily Express: "As far as I'm concerned, if anyone came in with less than £500,000, I wouldn't even bother looking at it, whether it's from Wolves, Leeds or Celtic."
"Right now, there is no offer on the table for Mark and I don't expect one to be there the next time I arrive at Tannadice. But it doesn't worry me. We have been fortunate enough to have signed Mark on a contract which goes through to until May 2008.
"He's an asset to the club. We rate him highly and we have a powerful hand because of his contract situation. It's not as if he is running out of contract, which would reduce his value."