Rooney is understood to be keen to move to Chelsea this month.
But Neville said: "This is not somebody who is going to go AWOL. I would be amazed if that ever happened.
"He's a street footballer, he's someone who, speaking to people this week, is training hard, wanting to play, wanting to do well, and keeping his professionalism about him.
"He went through a situation (a bust-up with Sir Alex Ferguson) two or three years ago if you remember.
"It was quite a public situation but he still continued to want to play football."
For the big stories and the banter follow us on Twitter: @tribalfootball