Reports in Spain claim Madrid president Florentino Perez is open to the idea of selling Di Maria at the end of the season, with Gareth Bale thought to be the club's top target to replace the Argentina international.
Di Maria has blown hot and cold this term, and Jose Mourinho is believed to be frustrated with the inconsistency of his performances.
United have question marks hanging over the future of their own wide-man Nani, and the Portuguese winger could make way for Di Maria.
But big-spending Paris St Germain have the financial muscle to match, and potentially even better, Sir Alex Ferguson - as they did last summer with Lucas Moura.
Di Maria was excellent last season as Real Madrid won their first league title since 2008, but he's struggled this term.
He's managed just four assists and four goals in 25 league appearances, while his pass completion percentage is one of the lowest in the team at 71 per cent.
The Argentine will likely still have a big role to play as Mourinho's side look to triumph in the Champions League, but this could be his final season at the Bernabeu.
Paris St Germain face a tricky second leg at the Nou Camp following their first-leg 2-2 draw at the Parc des Princes.