The Northern Irish coach insists the Uruguayan will not leave Anfield this summer after the Reds confirmed a bid for the striker had been rejected
The Gunners were preparing to make a bid of around €40 million for the 26-year-old, but Liverpool managing director Ian Ayre later confirmed that Arsenal's approach had been rejected.
Rodgers believes the north London club's 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," said the Liverpool boss.
"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 was included in the PFA Team of the Year.