Despite not handing in an official transfer request, the Uruguayan has made it clear that he sees his future away from the Premier League, with Real Madrid believed to be preparing an offer.
Rodgers has said that he is still in contact with the 26-year-old forward, who is currently competing at the Confederations Cup in Brazil, adding that he is not worried about the constant speculation.
"It's quite simple, the club is in complete control of the situation," the Northern Irishman told talkSPORT. "For me there is no real change in it. He's away with the Uruguay squad at the moment and we're messaging and what not.
"I will always listen to players. I always work closely with players and listen to their point of view but the biggest word is with the club.
"Sometimes interviews get put out there and highlighted, but parts of Luis' interviews have been about how much he loves Liverpool, but of course that doesn't get highlighted. It's something that happens. I'm quite relaxed about it."
Uruguay play Tahiti in their final Group B match on Sunday.