Manchester City are the latest club to be linked with a big-money move for the Uruguay international, but Ayre has dismissed the rumours of a summer transfer.
"There has been a lot written about Luis and he is a fantastic individual and we know he loves this club and the fans and has repaid anything he has done wrong in full," Ayre told BBC Radio Five. "We have always been supporters of Luis and he has stuck with us and is having probably the best season of his career.
"All the conjecture which went around last summer leading up to the January window was dispelled by the fact he signed a new contract. I think when you have a player like Luis, that is going to be a perennial issue.
"The important thing is we remain committed together. We have supported Luis through thick and thin and he has done the same by signing up to a new long-term contract recently."
The 27-year-old signed a new contract at Anfield in December 2013.