The Sky Sports News presenter appears as a regular on the Sky1 panel show with Andrew Flintoff, Jamie Redknapp, John Bishop and host James Corden.
"It would be nice to get Becks on," Thompson said at the third series launch. "A lot of football stars that I talk to are so well media trained but the one thing that this show does is disarm everybody.
"They're allowed to be themselves more and that's great, because you see a bit of a different side than the one you might read about in the papers or see in a sports interview.
"Big stars on this sort of show would be great because it would be a very different perspective - of which I think Becks would be one! There's loads, Jose Mourinho is someone I'd like."
Corden added: "I'd like [Arsenal's] Emmanuel Eboue. Hands down funniest footballer in the world.... He's just brilliant. He's exceptional.
"When Arsenal won the Emirates Cup - a friendly pre-season tournament that means nothing - everyone lifted the trophy and they're all slightly embarrassed... and Eboue did a lap of the ground just really going, 'Yeah!'"
> Click here for our full A League Of Their Own interview