Arsene Wenger reportedly had a bid of £30million plus adds-on rejected by the Liverpool board and Rodgers is determined to hold onto one of his prize assets.
Skipper Steven Gerrard signed a two-year contract extension on Monday and Rodgers inists Suarez will once again be lining up alongside him next season, "unless something drastic happens."
"He is a wonderful player and he is still very much a Liverpool player. No matter who the player is, nobody is bigger than Liverpool Football Club," said Rodgers.
"'Luis is a very important member of this squad and I am looking forward to working with him again this season.
"There has been lots of speculation about Luis moving to another club but, as I said, he is very much a Liverpool player.
"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."
Liverpool play an Indonesian All-Star XI on Saturday, although Suarez, along with defender Sebastian Coates and goalkeeper Pepe Reina, will not be involved as they enjoy an extended break following their involvement in the Confederations Cup.