The Reds have revealed an official bid from Arsene Wenger's side was dismissed, with the Uruguayan yet to confirm to the club he is looking for an exit from Anfield.
Arsene Wenger recently refused to answer questions regarding Arsenal's interest in Suarez, but Ayre has now revealed that Liverpool has rejected the Gunners' bid, with Suarez yet to confirm his desire to leave.
"We had an offer which is fairly public from Arsenal," Ayre told Bloomberg. "We said no to that offer, and as far as we’re concerned he turns up for training when he's due back. And we'll move forward on that basis.
"I've heard him say it would great to have an opportunity to play for Arsenal and likewise Real Madrid. But he certainly hasn't called me up and said he wants to leave.
"We get offers for lots of our players at different times. Unless we get to a situation where that player absolutely doesn't want to be here and we don’t want him to be here then that's a different kettle of fish.
"Right now we'd love to see Luis put on a Liverpool shirt for this season and beyond and we hope that once he gets back things will settle down."
Ayre also insisted that Liverpool is determined to keep hold of the former Ajax man, who scored 30 goals last season, and will be able to meet his ambitions of playing Champions League football in the future.
"This is an ambitious young player, he’s talked in the media about wanting to play in the Champions League and all these things," Ayre said. "It’s our job to convince Luis that this is the right place to achieve those things."
"I don’t think anyone will be against him at this point. He only needs to do what he did last season and everyone will feel he’s in the right place and he should carry on getting the support that he deserves and gets from Liverpool.
"We’d love to see Luis put on a Liverpool shirt for this season and beyond, and we hope that once he gets back things will settle down."