The Uruguayan's performances for the Reds have seen him linked with a handful of clubs, with new Bayern Munich coach Pep Guardiola said to be extremely interested in his services.
However, Ayre has stated that Liverpool have ambitions of their own and for that reason, they will not be allowing the 26-year-old to leave Anfield.
"To play at the highest level in the Premier League and European soccer, you need players like Luis and Steven Gerrard on your team," he told Sports Illustrated.
"So the last thing in our mind is selling Luis Suarez. He's not for sale. It's not something we're interested in."
Suarez joined Liverpool from Dutch club Ajax in January 2011.