This is according to the Express, who cite reports in Spain as claiming that Real Madrid boss Carlo Ancelotti is frustrated with Bale because of the Wales international's lack of tactical discipline.
Ancelotti is understood to be longing to re-sign former Los Blancos star Di Maria, who was one of Real Madrid's most influential players prior to his £59.7 million move to Manchester United in the summer.
Ancelotti keen to re-sign Di Maria
Real Madrid's manager would love to bring Di Maria, who has settled in well at Old Trafford, back to the Bernabeu - and United have the chance to use the Argentina international as a makeweight in a deal to sign Bale if Louis van Gaal gives the green light.
Recent reports have claimed that Manchester United are prepared to offer a world-record £90 million fee to sign the player who became the most expensive footballer in history after completing his £86 million move from Tottenham to Real Madrid in 2013.
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But Real Madrid would prefer a deal involving Di Maria instead of straight cash. The versatile South American was arguably the reigning European champions' most influential player last season, but was sold following the expensive acquisitions of James Rodriguez and Toni Kroos.
Bale's excellent debut season
Bale enjoyed a superb first season with Real Madrid, scoring 22 goals in 44 appearances, helping the Spanish giants end their 12-year wait for their tenth Champions League title in the process.
Bale, who currently earns a cool £300,000-a-week, scored in the final against Atletico Madrid - but it was Di Maria who was named Man of the Match.
Manchester United's current number seven is already a fan favourite at Old Trafford, but the chance to sign the athletic Bale - a contender for the title of world's third best player behind Cristiano Ronaldo and Lionel Messi - could prove irresistible for Van Gaal.
Both Bale and Di Maria are world-class players, though, and ultimately it's down to Van Gaal to decide which player is of more value to his team and philosophy.
Manchester United fans: would you rather keep Di Maria and leave Bale? Or sign Bale and sell Di Maria? Have your say in the comments below.