According to Spanish newspaper El Confidencial, Mendes will bring James Rodriguez to the Santiago Bernabeu this summer, paving the way for Di Maria to join United.
Rodriguez, also a United transfer target, has been one of the stars of the World Cup and currently leads the tournament with five goals as we approach the quarter-final stage.
Mendes, who often finds himself at the centre of most of football's biggest transfer deals, will negotiate on behalf of Rodriguez. The Colombian international is keen to leave Monaco to capitalise on his stunning form, with Real Madrid a contender.
And while Madrid boss Carlo Ancelotti does not want to lose Di Maria, he will relent if the defending Champions League winners can secure Rodriguez as a direct replacement.
Di Maria's valuation
United can afford to pay that, even after spending more than £50m on Ander Herrera and Luke Shaw. New boss Louis Van Gaal has up to £125m to spend, and is under instruction to get United back in the Champions League after last season's seventh placed finish.
Di Maria requested a new contract at the end of last season and wanted assurances over his future. He is yet to receive either from the club's hierarchy, even though Ancelotti has made it clear he still features in his plans. As well as United, Di Maria is a target for Juventus and Monaco too.
It looks like Madrid have all but sealed a move for Bayern Munich midfielder Toni Kroos. The final fee is expected to be somewhere in the region of €25m.
The Germany international had been linked with United.