"For me he is irreplaceable. You cannot find anyone there. It is so unique, his story, his qualities and what he has given to Leicester," Rodgers said.
"For us, it's more about the actual profile of what we want. I'll always look to have speed at the top of the field, but are there other attributes that we would look for? But to try to replace him – it's impossible."
Rodgers said there was a lot more to come from Vardy, who has scored over 100 league goals for Leicester.
"(He is) an incredible servant for the club, and still has a big contribution to make over this season and the next couple of seasons," Rodgers said.
"For the number of games we play, and the demands that is put on players...he is not going to be able to play to that rhythm and style every game.