Liverpool, seeded in the third pot in Thursday’s draw in Monaco, have been pitted against defending champions Real, Swiss side FC Basel and Bulgarian newcomers Ludogorets.
Liverpool last faced Real Madrid in 2009, where they followed up a 1-0 win at the Santiago Bernabeu with a 4-0 victory at Anfield to progress to the quarter-final stage of the competition.
“They're all tough groups but we’re pleased with the group and it’s particularly special to have got Real Madrid in the group,” Ayre told Sky Sports.
“We respect everyone but obviously we’ve great memories of games against Real Madrid so it’s very special for us.
“If you look at Liverpool as a football club, we’re five times winners and we’re playing against a team who’s just won it for the 10th time. It just makes for a very special group."
Asked what outcome Liverpool are hoping for in this season’s competition, Ayre replied: “The expectation is the same as it was before the draw and that is to qualify from the group.”
Manchester City face a seemingly difficult proposition after being drawn to play Bayern Munich, CSKA Moscow and Roma in Group E.
“It’s a very, very, tough group. They are very strong teams,” director of football Txiki Begiristain said.
When asked if he felt City had the hardest group, he replied: “I think so. It’s spectacular all the clubs try to play good football. It will be an amazing group.
“We are happy with the squad we have for this season. We’ve signed some very good players and we want to improve in the Champions League. We’ll try to win every game and we’ll try to play well.”