The Liverpool manager insists the Uruguayan striker will not leave Anfield this summer after the Reds confirmed a bid from Arsenal for him had been rejected.
The Gunners were preparing to make a bid of around 40 million euros for the 26-year-old, but Liverpool managering director Ian Ayre later confirmed that Arsenal's approach had been rejected. Rodgers believes the Gunners' bid for Suarez was well below his true value and remains eager to try and hold on to the wantaway forward.
"There has been lots of speculation about Luis moving to another club but he is very much a Liverpool player," Rodgers said. "We had an offer that was nowhere near what we value him at. Of course, he wants to work and play at the top level.
"But unless something drastic happens, he will be staying here. He has got three years left on his contract.
"He is a wonderful player, and still very much a Liverpool player. No matter who the player is, nobody is bigger than Liverpool football club.
"But Luis is a very important member of this squad and I am looking forward to working with him again this season."
Suarez scored 23 goals in the Premier League last season, second only to Manchester United's Robin van Persie, and he was included in the PFA Team of the Year.