Di Maria left Real Madrid for Manchester United back in 2014.
However, after a miserable year at Old Trafford, he was then sold to Paris Saint-Germain.
The Argentina international helped them win the Ligue 1 table last season.
And his eye-catching display in PSG's 4-0 Champions League win over Barcelona last month saw him linked with a shock move to the Nou Camp.
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Angel Di Maria could return to Real Madrid this summer
Angel Di Maria endured a nightmare season at Manchester United after leaving Real Madrid
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Lionel Messi has reportedly asked Barcelona chiefs to make signing him their top priority.
But Spanish outlet Don Balon claim Di Maria is wanted back at Real Madrid.
Club president Florentino Perez is said to have held personal talks with his former winger.
Angel Di Maria was a big hit during his time at Real Madrid
He said that, should the player wish to leave PSG, then Madrid would welcome him back with open arms.
Should he return it would plunge the futures of Isco and James Rodriguez into more doubt.
Rodriguez is wanted by Manchester United while Isco has been linked with a shock move to Barcelona.