Parker, who represented United between 1991 and 1996, has doubts about where the Real Madrid forward would fit into the United team.
Manager Jose Mourinho plays a notoriously defensive-minded style of play and demands all of his players to contribute at both ends of the pitch.
But Mourinho has confirmed that he is a fan of Bale and could attempt to land him in the near future.
Former England international Parker says that Bale’s approach would not suit the current United team and insists that the money could be better invested elsewhere in the team.
Parker, speaking exclusively to 888Sport, said: “You have to wonder where Gareth Bale would play.
“There is a lot of talk about getting him because everyone now has to go out and get an expensive player. But you have to look at where you can fit him in to get the best out of him.
“Gareth likes to play through the middle: he doesn’t like that wide role he had at Tottenham and prefers to step inside. So you’d have to adjust the team.
“I look at Bale and wonder if he’s a Jose Mourinho type of player because he likes a lot of touches, he wants to run with the ball.
“At Real Madrid he doesn’t track back so that’s something else he’d have to add to his game.
“Does he really want to play for Manchester United and have to track back because he hasn’t now for three or four seasons so long as he delivers going the other way.
“It’s all very well talking about these players but sometimes you have to ask yourself does the player suit the formation and does he even want to play there?”
Read the full 888sport interview with Paul Parker, including his thoughts on why Lukaku will have to overhaul his game under Mourinho.