The Red Devils have been regularly linked with a move to sign the Wales international over the past five seasons since missing out on his signature back in 2013.
Bale has won four Champions League titles, the La Liga crown and the Copa del Rey since his £85.7m switch to Real Madrid from Tottenham Hotspur.
However, the 29-year-old spent most of the 2017-18 season on the bench or sideline with injury to fuel speculation surrounding his future.
Bale ended the campaign with a flurry and came off the bench to score twice in Real Madrid’s 3-1 win against Liverpool FC in the Champions League final.
Zinedine Zidane’s resignation has given the Welsh forward a lifeline in the Spanish capital amid reported interest from Bayern Munich and Manchester United.
Sunday Times reporter Castles confirmed that Bale is a genuine target for Manchester United in the summer transfer window.
“Man United are definitely interested,” Castles told the Transfer Window podcast. “Mourinho tried to sign him last summer. Bale resisted and didn’t do anything to help or facilitate a move.
“If Real Madrid say yes to it, which they are likely to, and Bale says yes to it, which is undecided, Man United will need to redraw their transfer plans.
“They didn’t plan to sign an attacking player of his status.”
The Red Devils signed Brazil international Fred in a reported £52m deal from Ukrainian Premier League champions Shakhtar Donetsk earlier this week.
Manchester United made Portuguese teenage defender Diogo Dalot their second summer signing.
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