The Uruguayan striker continues to be linked with an Anfield departure this summer but Ayre says the Merseysiders will not prosper on the pitch if they look to offload their top players.
"To play at the highest level in the Premier League and European soccer, you need players like Luis and Steven Gerrard on your team so the last thing in our mind is selling Luis Suarez," he told Sports Illustrated.
"He's not for sale. It's not something we're interested in.
"I remember when [Fenway Sports Group] bought the team, John [W Henry] made a comment in the media: We don't want to just build a team to win but to keep winning. To do that you have to have a number of world-class players on your team."