Diario AS reported on Friday that the former Manchester United player could be used as part of the deal.
The French club sees it as a way of avoiding paying Neymar's transfer buy-out clause to the Spanish league and incurring a tax bill of over £62 million, the Daily Mail reported.
Paying the buyout clause means PSG pays Neymar £195 million and he then deposits the sum with the league to free him from his contract.
This method of payment could drag PSG into a dispute with the French taxman who could class the passing of the money by PSG to Neymar as taxable income, although the player could count the money as a gain in assets that he could subsequently offset as a loss when he then pays it to the league.
It also means all the money would have to be paid up-front whereas a more orthodox transfer could see the French side pay in stages.
PSG is keen to persuade Barcelona to treat the deal as a normal transfer and in order to persuade the Spaniards to cooperate PSG is willing to offer Barcelona a player.
Diario AS revealed on Friday evening that of a short-list of players Ligue 1 runner-up is prepared to include in the deal Di Maria is the one that most appeals.
Despite an interest in Di Maria Barcelona has so far said it will not negotiate and only accept the full buy-out clause paid to the league.