The 25 year old has been linked with a move to Premier League champions Manchester City.
However, Rodgers said: "There will be no bidding war. Luis Suarez is staying here."
The Uruguay international signed a new deal at the Anfield club in the summer.
Rodgers added: "If we lost Luis then we have no strikers, so I can't afford to lose anyone.
"He is certainly not anyone we want to sell or move. We want to add to the squad.
"We continue to work on what we want to achieve, Luis has already shown his commitment to club in the summer he signed a new deal. He is scoring goals here and working well.
"He is very, very happy here."