The report suggests the Red Devils will offer the Spanish giants £90 million to acquire the Welshman's services and bring him to Old Trafford.
Such a move would make sense given that Louis van Gaal's side have largely struggled when going forward in recent weeks; they've only managed one goal in their last four games.
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Therefore, United's offensive woes are the club's top priority for the winter transfer window. Bayern Munich duo Robert Lewandowski and Thomas Muller are similarly on the Red Devils' radar, though Bale appears to be their main priority.
United vice-chairman and transfer negotiator Ed Woodward expressed full commitment on bringing the Welsh superstar to Old Trafford before the start of the next season.
After David de Gea's failed transfer to Madrid over the summer, rumours suggest the clubs' relationship has been somewhat tethered, but Woodward believes he can still negotiate with the La Liga side even after the Spaniard's aborted the move.
Bale, meanwhile, has continued to struggle at Madrid, having largely played in the shadow of teammate Cristiano Ronaldo's shadow during his time at the Bernabeu.
It's little secret the pair share a frail relationship, and it's expected to stay that way until manager Rafael Benitez is able to find a way for both players to share the limelight.
There is no doubting Bale would add a fresh dimension to United's attack given his pace and clinical nature, though the issue remains whether the 26-year-old would be willing to return to England having yet to fully establish himself in a Real Madrid shirt.