Celtic goalkeeper Craig Gordon made 52 appearances for the Glasgow side last season.
Rodgers is expected to promote an attacking style at Parkhead, which requires his players to keep possession.
And, despite being a goalkeeper, Gordon is expecting to have to prove that he is capable of adapting to Rodgers’ chosen tactic.
"When a new manager comes in they have their own ideas and they want to play in a specific style, and that will include me," he said.
“I have to make sure I can show him I can adapt to that style of play, which I’m sure I can, but it’s about going out there and proving that and making sure I am in the team come the first game.
"Regardless whether anybody else comes in or if the goalkeepers remain the same at the club, the aim is the same – to go out and prove that I’m the best one here and to improve my own game.”
Gordon’s place in Celtic’s side appears to be under minimal threat, as he has had two solid seasons since moving to the Bhoys.
The Scotland international stopper has proven to be a good replacement for Fraser Forster and he has been a virtual mainstay in Celtic’s side.
Gordon made 52 appearances for Celtic last season, and he faced little competition for his spot in between the sticks.
Rodgers has already started making plans for Celtic, but improving his goalkeeper does not appear to be high up on his list of priorities.
The Bhoys, instead, seem more interested in bolstering their forward line and defence.
Celtic are reportedly interested in signing the likes of Liverpool defender Andre Wisdom and Sunderland striker Danny Graham.