Arsenal and Real Madrid have both been heavily linked with the Uruguay striker, but Rodgers is adamant that he will not be leaving Anfield ahead of the new season.
Suarez made 44 appearances last season, scoring 30 goals, but that was still not enough to secure Liverpool UEFA Champions League football, as they finished seventh in the Premier League.
Suarez is keen to play at the highest level, and has expressed his desire to leave.
Rodgers did concede that the club had received a bid for the 26-year-old, but revealed that it had not met their valuation of the player.
"There has been lots of speculation about Luis moving to another club but he is very much a Liverpool player," he 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."comments