Suarez currently tops the Premier League scoring charts with 22 goals this term.
Ayre told Sports Illustrated: "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's not for sale. It's not something we're interested in.
"I remember when they (Fenway Sports Group) bought the team, John (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."