Now Liverpool managing director Ian Ayre has confirmed that they received, and rejected, a bid from the Gunners.
"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. We'll move forward on that basis.
"We get offers for lots of our players at different times. Right now we'd love to see Luis put on a Liverpool shirt for this season and beyond. We hope that once he gets back things will settle down."
It has been reported that Arsenal will increase their offer after making Suarez their top transfer target this summer.