The Uruguayan's desire to leave Merseyside this summer has been clear from various interviews he has given over the last few weeks, but Liverpool have emphasised they do not intend to sell the player and rejected an offer - understood to be £30million - for him from Arsenal.
Rodgers, who has stuck by the striker through some controversial moments, insists he is not worried the issue will drag on and interfere with his pre-season plans.
"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 told the Liverpool Echo. "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.
"There can be as much speculation as you like, but there has been nothing beyond that."
Rodgers was unimpressed with Arsenal's valuation of the player, especially in light of the amount of money Paris St Germain paid to take Edinson Cavani from Napoli.
"It was an offer for what they (Arsenal) considered his value and worth," said Rodgers. "Obviously for a player of his quality, when you consider that Cavani has gone for £55million you know... 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."
Rodgers also spoke of how he has been let down by Suarez over the Patrice Evra race row and his subsequent bite on Branislav Ivanovic only to show continued loyalty to the Uruguayan, and he feels Reds players and supporters are also owed a debt of gratitude.
"It's not about me or the club, I think it's the supporters and his team-mates for what they gave him," said Rodgers.
"What I do is the same for anyone. My success is not just about trophies, although hopefully when I finish my career I will look back on having won things.
"For me it is about more than that. It's about making people better people and supporting them when they need it. Luis doesn't need to show me anything because that's what I do.
"For me it's about the great supporters we have. The backing they have given him is absolutely brilliant.
"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."
This week Liverpool confirmed Suarez had been named in the 27-man squad for their pre-season tour of Indonesia, Australia and Thailand, saying he was one of three players - all given extended leave due to being involved in last month's Confederations Cup - who would be joining the party later in the tour.
Speaking to reporters at a press conference in Jakarta on Thursday, Rodgers said: "Luis Suarez 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.
"Luis is a very important member of this squad and I am looking forward to working with him again this season after he had such a fantastic 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. He's one of the top strikers in the world.
"Of course he wants to work and play at the top level. But unless something drastic happens, he will be staying here."