Thompson admitted he was asked earlier this year to make it clear whether the Tayside club was for sale. United recently cleared their outstanding bank loans and have raised £5m from the sales of Ryan Gauld to Sporting Lisbon and Andrew Robertson to Hull City.
Thompson has insisted he has no intention of selling up as the club bids to keep progressing under manager Jackie McNamara.
"I'm not interested in selling," he said. "I was approached by a third party on behalf of a potential investor in England, who wanted to know whether I was interested in selling the club.
"I told them that the club was not for sale. We have worked too hard to get us to where we are to sell up now. We're free of debt from the bank.
"We own Tannadice Park and the Gussie Park training facility across the road from the ground and we are about to redevelop that with a new European two-star artificial surface. "The bank is off our back now They have no say in who we sell and they do not take a cut of any of the players we sell."
United finished fourth in the SPFL Premiership and reached the final of the Scottish Cup last season in McNamara's first full term at the helm. "The fans have bought into what Jackie is doing with the team and the style of football we play," Thompson said. "Our season book sales are our highest ever and we are working on another of couple of big things at the club for the future. We've come a long way."