The 48 year-old has taken over the managerial reins twice this season as the Seasiders have watched Ian Holloway leave to join Crystal Palace and more recently Michael Appleton jump ship and take over at north west rivals Blackburn.
Although his second stint in charge has seen three losses the former midfielder believes that he is the right man for the job.
Nigel Adkins has now become the front runner for the position after becoming the latest Premier League manager to get the boot on Friday, with Southampton bringing in Mauricio Pochettino.
"There's always going to be speculation," said Thompson.
"I'm in charge - temporary charge - for 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.
"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."