Suarez tried to force through a move away from Liverpool after the club's failure to qualify for the UEFA Champions League last season.
The forward was the subject of two bids from Premier League rivals Arsenal in August before signing a new contract in December.
"We love having him as part of the club and I know he loves being here so we would expect that to carry on," Ayre told BBC Radio Five.
"We don't want to sell Luis Suarez and we've been consistent with that in every transfer window since he came here.
"We are a team on the up and he is a fundamental part of what we are trying to achieve.
"We would never wantonly sell Luis Suarez."
Suarez found himself at the centre of a racism row with Manchester United defender Patrice Evra, before biting Chelsea's Branislav Ivanovic at the end of last season.
"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," said Ayre.
"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.
"We would expect that to continue, but we'd also expect people to come in and rattle our cage every transfer window."
