Reports have suggested Manchester City were weighing up a £40million bid for the Uruguay international when the transfer window reopens. City have distanced themselves from that link, but in any case Rodgers has every intention of hanging on to his leading scorer and only fit senior striker.
"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."
Rodgers added: "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."
Suarez only signed a new long-term contract in the summer and while Rodgers knows he needs to strengthen his forward line in January he does not believe he has to do so in order to convince the South American to stay.
"We just continue to work and stay focused on what we try to achieve," added the Reds boss.
"Luis has already shown in the summer his commitment to the club, he's signed a new deal.
"I think you've seen up until this point he's in a great moment in his footballing life here at Liverpool: he is scoring goals and working well.
"I'll just continue to communicate with all the players and Luis in particular. Like I say, he's very happy here."