As exclusively revealed by Goal.com, the Reds' Premier League rivals, Manchester City, are keen to offer the Uruguayan, who has scored 22 Premier League goals so far this season, the Champions League football that he wants.
With Liverpool seventh in the table, qualification for Europe's top competition is unlikely but Ayre was categorical in his rejection of any potential sale.
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"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."
Ayre also discussed his satisfaction with the success of the club's work in the winter transfer market, enthusing: "We were very pleased with the most recent window in January with Philippe Coutinho and Daniel Sturridge. It's a combination of skills and people and processes that bring us to what we're trying to achieve.
"I think the fundamental shift particularly around player acquisitions and disposals was that we took the view that it needs to be more of a science. Your biggest expenditure line can't be the whim of any individual.
"It's a combination of old-school scouting and watching players - and that's Brendan [Rodgers], his assistants, our scouts - with statistical analysis of players across Europe and the rest of the world.
"I think we've had relatively good success since we deployed that methodology. We're getting better all the time. Just as you think our football is getting better, our transfer activity is getting better."