The Reds have failed to qualify for Europe's top competition since their second-place Premier League finish in 2008-09 but Ayre feels that it could take time for Brendan Rodgers to reshape the club enough to reach the elite again.
|2/1||Liverpool are 2/1 with Bet365 to finish in the Premier League top four in 2013-14
"This football club is steeped in the tradition of the European Cup. That's where everyone wants to be from the owners down.
"Our ambition is to get there. Whether we do that in one year, two years or three, we will see. That's where Liverpool should be."
After swapping Kenny Dalglish for Rodgers, the Reds improved to finish seventh in 2012-13 and Ayre urged continued patience from fans following a significant shift in playing style.
"We made a big change a year ago with the ambition of getting Liverpool back where they should be at the top of football," he added. "We changed the manager, we changed the style of play and we changed some players. We said we wanted to build something here.
"Rome was not built in a day. If you could do it in one day, then everybody would do it."