In several recent interviews in his homeland, the 26-year-old has repeated a desire to leave the Premier League club and play in Spain, blaming the British media for making his life impossible in England.
Liverpool have insisted that the talismanic striker, who was last season's second top scorer in the League with 23 goals, was not for sale.
"It's quite simple, the club is in complete control of the situation," Rodgers said when asked about Suarez, who is currently on international duty at the Confederations Cup in Brazil.
"I will always listen to players. I always work closely with players and always listen to their point of view but the biggest word is with the club," Rodgers added.
"We're in a situation where we've got a player who we don't want to lose. We're trying to build something here and he's a very important part of that and because of the type of player he is, he will always give his best."
Suarez, who signed from Ajax Amsterdam in January 2011, received a 10-match English domestic ban for biting Chelsea's Branislav Ivanovic towards the end of last season.
His eight-game suspension the previous season for racial abuse has meant that stellar performances for Liverpool have been offset by a barrage of criticism in the media for his regular misdemeanors.
"Sometimes interviews get put out there and highlighted but parts of Luis's interviews have been about how much he loves Liverpool, but of course that doesn't get highlighted," Rodgers added.
"It's something that happens. I'm quite relaxed about it.
"What I know is that the support Luis has had from the people here in Liverpool, the city and the football club, has 0been phenomenal and I know he feels that and respects that."
Rodgers added that midfielder Steven Gerrard was making good progress from last month's shoulder surgery and the Liverpool captain would be ready to train with the club at the beginning of the season.
Rodgers also expressed his delight at signing Spain youth international Luis Alberto from Sevilla.
The 20-year-old has signed a long-term contract with Liverpool after passing a medical, with the deal still subject to international clearance.
Alberto, capped at several levels of youth football by Spain, spent last season on loan with Barcelona B, where he scored 11 goals and collected 17 assists in 38 appearances.
"We are all delighted that Luis has decided to join Liverpool," Rodgers said.
"He has the correct footballing profile and mentality to be a Liverpool player.
"I look forward to working with him to develop his talent and he joins a group of young, exciting players at our club."
Alberto admitted he had been surprised when he became aware of Liverpool's interest, but had no doubts about accepting their offer.
"I feel like I'm in a bubble at the moment," he said. "For me Liverpool is a top team. I feel like I am dreaming and I want to enjoy it to the full.
"I feel very excited, I've never felt so excited before but I'm very happy. I think I am the happiest man on earth.
"I was surprised (when Liverpool showed interest in me). You never expect this to happen to you. But as the deal moved forward, I became very happy and I wanted to come to Liverpool.
"I have come here to enjoy moments with the supporters – and I know the supporters will help me to never walk alone.
"I hope that between us all we can make this club one of the greatest in the world, once again."
Alberto came through Sevilla's academy and made his first-team debut in April 2011 before going out on loan.