Addressing potential replacements, Thompson has tipped current Sky Sports presenter Julian Warren for the role.
But he believes any potential candidate would have to carry a certain personality to succeed Stelling in the hot seat.
“Julian Warren presents the Soccer Show on Tuesday and Wednesday nights, and he’s always been very capable.
“He’ll probably be up there in terms of replacements, but he’s not Jeff Stelling, and he’d be the first to say that. But he’s a great lad.
“With the likes of Kammy [Chris Kamara] and Roy Keane, you have to be of a certain personality and while they’re great pundits, I’m not sure they have what’s needed.”