No formal offer has been made, although Barca boss Luis Enrique reportedly sees him as a perfect fit for his side.
The Argentine has failed to settle in England despite a good start, following his big money move from Real Madrid last summer and now reportedly wants out after just one year.
That has allegedly sparked the interest of La Liga champions Barcelona, who are looking to strengthen their squad following a treble winning campaign last season.
According to the report by Sport, the two clubs aren't into deep negotiations over a possible sale yet, but the Catalans have had initial talks with both the player and his representatives.
And it seems that Di Maria would prefer to move back to Spain ahead of anywhere else, which is unsurprising given the success he enjoyed with Madrid before the move to Old Trafford.
A move to the Nou Camp would also see him link up with compatriot and close friend Lionel Messi, making a deal all the more likely.
One potential stumbling block may be price, with United likely to want to recoup some of the money they paid for him. Barcelona of course, can’t sign players until January either, meaning that Di Maria would be staying in England until then at least anyway.