Suarez's future has been the subject of much debate this summer with the striker making it clear in several interviews given while back in South America that he wants to move on and play for a Champions League club.
Real Madrid were thought to be the frontrunners to land him but they have yet to make an official offer and only the Gunners' £30m bid, which was swiftly rejected, has been forthcoming.
Rodgers says that bid is nowhere near the amount the club value him at and the controversial forward should stay at Anfield to pay back the fans and his team-mates, who have stood by him through thick and thin during his two-and-a-half seasons in the Premier League.
"It's not about me or the club, I think it's the supporters and his team-mates for what they gave him," Rodgers told the Liverpool Echo.
"They have stood by him through thick and thin, and through all the traumas he has gone through over the last couple of seasons.
"If there is anyone he owes it's them and his team-mates, who have fought beside him, certainly not me."
Rodgers also reiterated that Liverpool are in control of Suarez's future and hinted even if an offer of £55m came in they may not accept it.
"I don't want to set a deadline or put a date on it but this is not something that will run too long," he added. "We are totally in control of the situation. It is one where we don't have to sell. He has got three years left on his contract.
"We are prepared to get some players in and spend money without having to sell Luis Suarez. The reality is that we have had one offer.
"It was an offer for what they (Arsenal) considered his value and worth. Obviously for a player of his quality, when you consider that (Edinson) Cavani has gone for £55m. Luis is up there in that bracket of top talent.
"Obviously it was an offer we didn't deem worthy of the talent and even if they came back with that kind of amount (£55million) there's no guarantee he would be sold even for that because we are trying to build something here."