City are reportedly lining up a £40m move for the Uruguayan, who has hit 11 goals in 16 appearances so far this season.
But Suarez, who only signed a new deal with Liverpool in the summer, will not be going anywhere, according to Rodgers.
"There will be no bidding war. He's staying here," said the Northern Irishman. "If we lost Luis then we've got no strikers. I don't think we can afford to lose anyone.
"He's certainly not someone we want to sell or move on. He's been a brilliant player to work with and we want to add to our squad, not take people out of it, especially a world-class player."