The Reds were drawn alongside the reigning European champions in Group B of the 2014/15 version of the competition and Ayre suggests it is an exciting test for the Merseyside outfit.
"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."
Of Liverpool's hopes in the Champions League, Ayre added: "The expectation is the same as it was before the draw and that is to qualify from the group."
Also in Group B are Swiss giants FC Basel and Bulgarian minnows Ludogorets Razgrad.
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