Rodgers has poured cold water on a return to the Premier League as he underlined his lack of desire to leave Parkhead.
Rodgers told BBC Radio Scotland's Sportsound programme: "There's nothing really in it. I have always said I'm extremely happy here. I have three years left on my contract. I am loving every minute of being at Celtic from a professional perspective but also my life up here.
"I have a number of years left as a manager. I am 45, I probably look a lot older but, 45, and I'm enjoying my position here. It's a huge privilege for me to manage Celtic. It's a huge club with pressure and that's all I concentrate on.
"Having played against them and worked against them and lived most of my life in England, I know the status of the club.
"They want to get back towards Champion League football and when Arsene leaves they will look to move in a different direction, I'm sure.
"It's a fantastic club but, for me, my only focus is on Celtic and doing the very best I can for them."