The England hooker, a World Cup winner in 2003, still has two years remaining on his existing Northampton contract.
But he is known to be keen on a move across the Channel - for lifestyle, as much as rugby reasons - with Brive and Toulouse heading the queue of possible destinations.
Thompson's immediate priority is for Northampton to secure a quarter-final place, which they would guarantee by completing a hat-trick of Heineken Cup home victories over Biarritz, having beaten them in 2000/01 and 2002/03.
A losing bonus point could even be enough for Saints as one of two best runners-up across all six pools, but head coach Paul Grayson said: "The focus is on winning the game.
"We are going out to maintain our home record against Biarritz. We could go out there, score four tries and shut them out to top the table.
"I am not saying that is impossible or very probable, but we are going out to play and win."
Centre David Quinlan has recovered from a hand injury to partner Ben Cohen in midfield, but prop Tom Smith is sidelined due to a sore wrist, meaning a chance in the front-row for Chris Budgen alongside Thompson and Pat Barnard.
Grayson added: "It would be nice to make it three out of three against Biarritz at home.
"I have played in some good victories against them, and I know what we do on the pitch reflects how much noise comes out of the stands."
Llanelli Scarlets head into Sunday's Pool Five finale against Stradey Park visitors London Irish having already clinched a quarter-final place and home advantage. Their aim now is simply to secure a sixth successive victory.
Wales failed to provide a quarter-finalist during each of the past two European campaigns, but Llanelli spectacularly ended that barren spell by recording stunning victories against Toulouse and Ulster (home and away) after launching the pool by toppling Irish at the Madejski Stadium.
Scarlets number eight Alix Popham said: "We can definitely do something in this competition now.
"It is great for Welsh rugby that we are through and we are at home in the last eight, which makes a massive difference."
Irish, already eliminated from the tournament, make several changes following last Saturday's narrow home defeat against Toulouse, including call-ups for centre Nils Mordt and wing Justin Bishop, who replace injured duo Gonzalo Tiesi and Dominic Shabbo.
And the Exiles have announced New Zealander Riki Flutey's departure when his current contract expires at the end of this season.
Irish rugby director Brian Smith said: "We are disappointed that Riki has decided to move on at the end of his contract.
"His decision not to re-sign has come as a big surprise, so we will take some time to review our squad and decide if we will go after another big midfield signing.
"While we were able to match his financial demands, he has decided to leave for other reasons."
In Sunday's other Heineken Cup games, Ulster visit Toulouse, while Italian outfit Overmach Parma hope to break their Pool Six points duck when they host Border Reivers.