The Reds boss dismissed reports speculating about a £40million bid from Manchester City - who have distanced themselves from the rumours - in January, insisting the subject was not even up for discussion and the striker not for sale.
"He is not for sale. There will be no bidding war. He's staying here," said Rodgers. "I don't have that fear (his head will be turned) with Luis. He has already shown in the summer his commitment to the club, he's signed a new deal."
Rodgers also expressed his confidence contract discussions with another of the club's prized assets, 17-year-old Raheem Sterling - who made his England debut in the friendly against Sweden on Wednesday night - would be resolved "without issue".
The teenager, who turns 18 next month, has 18 months remaining on his current deal and is also reportedly attracting interest from other clubs but the player last weekend dismissed claims any hold-up was down to a disagreement over wage demands. However, Suarez remains the one player Liverpool cannot afford to lose.
He added: "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 and he's very happy here. He's certainly not someone we want to sell or move on. If we lost Luis then we've got no strikers. He is a very important member of our team and I think you see he is really enjoying playing in this way of working and obviously his goals count for that.
"But he still has improvements to his game to make himself and we're looking on the training field to improve our performance to help us win games. We want to continue to build the group around him. We are in the very early stages of trying to form something at the club and Luis is an integral part of that. So for us it is not even a discussion point. I can respect that, because of his level, people will want to speculate but he's very happy and I'm very happy to work with him."
Of Suarez's 11 goals this season eight have come in 11 Barclays Premier League matches, making him joint top scorer with Manchester United's £24million summer signing Robin van Persie. His league tally since joining Liverpool from Ajax for £22.75million in January 2011 is impressive with 24 in 55 matches.
Sterling is the other player at Anfield to have made an impact this season as his rapid rise continued with a first England senior appearance. Rodgers does not envisage the teenager's newly-elevated status will prove to be a barrier in negotiations over a new contract.
"I think it will be pretty straightforward," he added. "That will be resolved. There won't be an issue there. I think Raheem himself, his representatives and his family know he is at the best club he could ever be at in terms of his development short and long-term."