The Red Devils have been heavily linked with a move to sign the Wales international over the past few seasons but a deal has always failed to materialise.
However, the situation could be different this summer given Bale struggled to hold down a regular starting spot in the Madrid side under Zinedine Zidane last term.
Bale came off the bench to score twice in Real Madrid’s 3-1 win against Liverpool FC in the Champions League final in Kiev last month.
The Wales international would be a big-name signing to keep the Manchester United supporters on side and help to close the gap on their bitter rivals Manchester City.
Pogba endured a difficult 2017-18 season after the France international appeared to fall out with Red Devils boss Jose Mourinho over his best position in the team.
Reporter McGarry suggested that a swap deal between Manchester United and Real Madrid could happen this summer with Bale and Pogba heading in opposite directions.
“Modric needs to be replaced long term,” McGarry told the Transfer Window podcast.
“Maybe Pogba could be part of a deal that brought Bale to Old Trafford. I’m not sure Mourinho would be too sad if he got Bale instead.”
Manchester United finished in second place in the Premier League table last term before losing 1-0 to Chelsea FC in the FA Cup final.
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