Gerrard made his Kop debut in 1998 and will be 33 in May. But the England midfielder has shrugged off his old injury problems by playing every minute of every Premier League game this season.
And Rodgers added: "He's an incredible player. And I've never thought about replacing him because if we look after him I know he has a good few years left in him yet.
"Yes, there becomes a time where every player stops and the next one comes in, and it'll be up to us to look over the next number of years to bring in the dynamic player that can fulfil what he's done.
"But it's not in my thinking now, purely because I don't need to think about it."