Mourinho is among the favourites to succeed Sir Alex Ferguson following his retirement announcement this morning.
Big Ron told talkSPORT: "We know Jose Mourinho is desperate for the job, but he might be considered a little too outrageous for them.
"There has to be a good style of play as well. Manchester United fans are brought up with a certain style of play and it shouldn't be overlooked that whatever they've won, they have won it in style.
"That may, to a certain extent, count against Mourinho, who is a little bit more pragmatic in the way he plays the game. I would say if it's a straight run between the pair of them then it's going to be (David) Moyes."