In the wake of Saturday's 2-1 derby loss to Manchester City, Parlour spoke of the United team and how he now feels England captain Rooney is not necessarily an assured starter.
"Rooney is playing with good players now. He is not guaranteed to play," he said on Sky Sports' Goals on Sunday show.
"Jose will look at the situation - I thought Rashford should have started myself.
"He scored a hat-trick in the U21s, he's in great form. He always seems to have that little bit extra when he comes on to the pitch. So I would have started with him. I know he made the half-time substitution and he came on.
"But Rooney, like when playing for England, he was playing in that 'hole' a little bit too deep.
"So, Rooney now will be looking at himself. But he is a top pro and I am sure he will be working hard and trying to get the best out of himself. As you get older, you do lose that little bit of pace, but he is a top player and I am sure he will come good again.
"It is a shame because the spotlight is always on Wayne Rooney. He does get a lot of criticism, but he is a top-class player and he has to deal with that."