Neville admits he was taken aback when Sir Alex Ferguson announced Rooney had asked for a transfer last season.
He told The Sun: "We were live on Sky when Alex Ferguson announced that Wayne Rooney had asked to leave.
"Everyone was surprised but I am hopeful he will stay — Wayne and United go together.
"I am aware of how big the club is, you can achieve all your ambitions there. He has to make his own mind up but the club will also play a part in it — United never panic in these situations."