The caretaker boss has now overseen three straight defeats since taking over from Michael Appleton - the latest a 2-1 loss to the Championship leaders.
Thompson wants the job full-time, but Nigel Adkins is a possible alternative following his dismissal by Southampton.
"There's always going to be speculation," said Thompson. "I'm in charge at the moment and until I hear anything different I'll keep going along.
"But I think it needs sorting, especially for the lads because they need stability around the club.
"The players hear all the speculation, it needs sorting out. There are lads out of contract, there's lads who need the contract sorting. I'd be lying if I said it wouldn't be unsettling for them. Until we hear different we've just got to make sure we get them right.
"I've said from day one that Karl Oyston will make the decision and hopefully the right decision for Blackpool Football Club.
"I want to be number one - of course I do. I've always said I'm ready, I'm ready to be number one but whatever Karl decides to do I'll back him 100%, with whatever role I have at Blackpool."