The Championship outfit is expected to announce Paul Ince as its new boss later today and Thompson has his heart set on being his deputy.
"It's something I want to do," Sky Sports News quotes him as saying. "It's quite difficult stepping in as number two.
"As much as you try and do things right, you always know that this time next week you might have your arm round a new manager as his assistant.
"I'll just have to see what happens. I think Paul wants me to work with his team. I'll keep my head down and work as hard as I can for him, but further down the line, I want to be number one."
Ince, who has not managed since leaving Notts County almost two years ago, will reportedly be confirmed as Blackpool boss at a press conference later today.