His club may not have any great need to sell, but the departure of Ryan Gauld - spirited to Sporting Lisbon in a deal worth £3m and believed to contain lucrative sell-on clauses - shows their arms can be twisted if the price is right.
Come knocking with the right amount of cash and Thompson, as he hinted very strongly last night, will be ready to play.
West Ham United have had two bids turned down for Andy Robertson, the 20-year-old left-back voted PFA Scotland Young Player of the Year and given a cap for Scotland less than a year after moving from Queen's Park, with the latest offer understood to have been worth £1.5m.
An auction is already brewing. Everton have been monitoring him for months and there has been talk of West Bromwich Albion, Sunderland and Newcastle United showing an interest.
Sunderland have already been thwarted in a past attempt to sign one of United's academy graduates. They agreed a £600,000 fee for John Souttar last October only for the central defender, still just 17, to turn them down after travelling to Wearside for a look around.
Queen's Park Rangers were another club regularly represented at Tannadice towards the end of last season and they certainly have money to spend following their promotion to the Barclays Premier League.
Stuart Armstrong, an attacking midfielder growing in stature and reputation, was the subject of several reports filed back to HQ at Loftus Road. It stands to reason QPR, along with others, must have noted the form of Robertson, Souttar and the increasingly impressive Nadir Ciftci along the way.
While the speculation mounted, United quietly tied most of these guys down on new contracts to protect their value. Within weeks of each other at the end of last year, Gauld, Souttar, Armstrong and Ciftci had all extended their agreements until May 2016.
Thompson believes the sale of Gauld to Sporting, who have inserted a €60m buy-out clause in his six-year contract - will enhance the reputation of United's youth department in the eyes of scouts and sporting directors around the world and was clear when asked if he believes the headline-grabbing transfer will open up the club to more European sides on the search for new talent.
"I think so," he said. "It puts us on the map in Europe and we have a lot of young talent at the club just now. I hope they can kick on and have another successful season.
"It is difficult [to hold on to players], but it shows you the great work that has been done by our manager, Jackie [McNamara], and the whole management team. It shows we have done something right with the youth structure and it is of great credit to all of them that there is interest in our players.
"It's never easy to let one of your best players go, but it was a fantastic deal for the club and a great opportunity for Ryan.
"We have said now for a number of months that we don't have to sell anybody unless the deal is right for our club. Once Ryan found out who the club was, though, he was very keen to go and speak to them."
For the likes of United, the sell-on can be just as lucrative as the initial transfer fee. Should "Baby Messi" prove to be as good as the real thing and cause that €60m buy-out clause in his Sporting contract to be invoked, United will be rolling in it again.
Thompson would not confirm the figures agreed in negotiations with Sporting, but it is quite possible they have retained a percentage of ownership rights over him in keeping with a number of transfers conducted abroad.
"I cannot discuss the confidentiality of the agreement with Sporting, but we are very pleased with the contract that we have got," reported Thompson.
"If he is successful and moves on further down the line, we will get benefits from that as well. They were the first club to come to the table and have proper negotiations with us. We thought it was the right deal for our club and a fantastic opportunity for Ryan.
"He is a pretty quiet lad and he will get on with it. I think he will settle in well. It's a great opportunity and a great club that he has gone to.
"I think he has handled the pressure with all the speculation about other clubs over the last year very well and I think he will continue to handle it very well. He's only 18, but he's quite mature for his age."
McNamara must have concerns over what lies next, though, as he plans for next season. He is discussing transfer targets of his own with Thompson, but the word from Dundee is that the sale of Gauld will not have any dramatic effect on his budget.
"We have restructured our finances at this club in the past few months," said Thompson. "Jackie and I were chatting this morning about players we would like to bring in for next season and we will keep working quietly in the background with regard to that."
Meanwhile, United have recruited David Southern from Hearts as their new general manager.
Southern spent the last four years as managing director at the Edinburgh club and was in charge when they collapsed into administration.
"Now that the club is safe and the revival is well underway, I feel my work here is complete," he remarked.
"I feel, both personally and professionally, that it is the right thing to do in my career and I am looking forward to the new opportunity that lies ahead."
Ann Budge, the chairwoman and chief executive at Tynecastle, insists he leaves with her best wishes.
"Whilst Hearts is in a period of revival, I fully understand why David would wish to continue to develop his career and grasp this opportunity to remain in the Premiership with one of Scotland's leading football clubs," she said.