The Uruguayan international stated that he wanted to leave the club following a difficult end to the last campaign, and has been the subject of a £30m bid from Arsenal, which was rejected by Brendan Rodgers's side.
However, Ayre insists that the Reds have no plans to allow the striker to leave Anfield this summer.
Ayre told Grandstand: "Our expectation is he'll be pulling on a shirt for Liverpool and carrying on with his contract.
"We've been pretty consistent on Luis. He has made some comments in the media, we've made it clear it's not our intention to sell him, he has three years left on his contract.
"We did have an offer, only one offer, from Arsenal. We rejected that offer and they haven't made a subsequent bid."
Suarez ended last season with a 10-game suspension after biting Chelsea defender Branislav Ivanovic.