Liverpool plan to offer Suarez new deal
Suarez, 25, signed a five-and-a-half year contract on his arrival in January 2011, but the Reds are keen to extend that deal following reported interest from big-spending French club Paris Saint Germain.
The former Ajax star has endured a difficult season after being banned for eight games for racially abusing Manchester United defender Patrice Evra.
But his form has remained strong and he caused concern on Merseyside by reportedly suggesting he would be interested in linking up with international team-mate Diego Lugano at PSG.
Liverpool are keen to stave off any interest from elsewhere and Ayre said: "Listen, he's got a contract until 2016, he has said he wants to stay. I am sure (technical director) Damien (Comolli) will be speaking to his agent.
"Who wouldn't want Luis Suarez? He is absolutely fantastic. He is such a popular member of our team.
"But they are the things we talk about behind closed doors, and we will further that discussion when it is right and proper.
"Luis is a vital and important part of our set-up, and long may that continue."