Spanish newspaper Marca, as quoted by Metro, is reporting that the Wales international is a firm transfer target for the Red Devils board as they consider strengthening their squad in the off-season.
Bale has been regularly linked with a move back to the Premier League since his move to Real Madrid from Tottenham back in the summer of 2013.
Manchester United were also touted as a possible destination for the Wales superstar before he ended up signing for Real from Spurs.
The same report says that Manchester United chiefs are keen to make a big-money move to sign Bale in the summer, but Mourinho himself is not keen on a deal for Bale.
Bale has struggled with a number of injury problems since his move to Spain and has only made eight appearances in La Liga so far this season due to his latest fitness issue.
He has, however, still managed to score seven goals and make three assists in all competitions for the Spanish side so far this term.
Meanwhile, Manchester United take on Yeovil Town in the fourth round of the FA Cup on Friday night.
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