Goal understands the Gunners have lodged a £42 million bid for the Uruguay international, who has made no secret of his desire to play in the Champions League this season.
|16/1||Liverpool are 16/1 with Coral to win the title
But the unsettled striker was still given a rapturous reception by the travelling Reds support during Wednesday's friendly win over Melbourne Victory, and Rodgers believes this will play on the striker's mind.
"The support he has received from the supporters and the people of the city of Liverpool has been unrivalled," the former Swansea boss told reporters. "In this period of time he's missed a lot of games for the club through various reasons.
"The people have stood by him, like a son and really looked after him.
"Whatever happens in the coming weeks that will be in his mind because it's something you can never forget."