The Red Devils have been regularly linked with a move to sign the Wales international over the past two or three seasons.
Bale is facing an uncertain future at Real Madrid amid reports over an overhaul at the Bernabeu outfit in the summer transfer window.
The 28-year-old could be sacrificed along with Karim Benzema as Real Madrid manager Zinedine Zidane looks to give his squad an overhaul.
Bale has won three Champions League titles, La Liga and the Copa del Rey crown during four and a half seasons in the Spanish capital.
However, former Manchester United defender Parker believes Bale would be making a huge error if the Welsh winger moves to Old Trafford this summer.
“United will make some big signings which is great in one way but you wonder are they becoming a team?” said Parker, speaking exclusively to 888Sport.
“You have to wonder too whether someone like Gareth Bale would fit in? Where would he play? He’s not a wide player anymore and likes to do his work through the middle.
“There are a lot of players who are already placed in the middle and the problem is a need for someone who is happy to provide width and stay out wide.
“Martial wants to come in. Rashford wants to come in and is very good at it. Bale would just be another player who wants to be a centre-forward.
“From a marketing side it makes sense but you have to ask if Gareth Bale would be comfortable there and given freedom.
“He’s not a player to track back and his first thought is always offensive and to run at people with pace and will he be given a chance to do that?”
Manchester United signed Chile international Alexis Sanchez from Arsenal in a swap deal in the January transfer window.
The Red Devils finished in sixth place in the Premier League table last term but won the Europa League and the League Cup in Jose Mourinho’s first season in charge.
The 20-time English champions haven’t won the title since 2013 when Sir Alex Ferguson got his hands on his final top-flight crown.
Read the full 888sport interview with Paul Parker, including his prediction for the Manchester Derby this weekend
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