According to Daily Express, PSG have made £40m bid for Di Maria and in turn United have enquired over the availability of Cavani.
United are believed to value Di Maria close to £50m, however it is reported that the Red Devils are happy to do a straight swap without any cash being exchanged.
The Premier League giants purchased Di Maria for British transfer record of £59.7m last summer, but the Argentine international failed to live up to his price tag after scoring just four times in his debut season.
Daily Express reports Van Gaal was keen to hold onto the 27-year-old but is now happy to let the former Real Madrid man leave should he receive Cavani in return.
Manchester United face PSG in a pre-season friendly in Chicago on July 26, and it is understood a deal could be finalised then.
Angel di Maria transfer: Man United flop AGREES five-year deal with PSG, £42.8m FEE to be finalised
Man United goalkeeper set for Old Trafford STAY despite Real Madrid interest
Man United eyeing INCREDIBLE £75m double summer swoop as spending SPREE continues