United and Tottenham had bids accepted for Juventus forward Dybala before the Premier League transfer window shut last Thursday.
But neither team could agree personal terms with the 25-year-old forward, whose demands over salary and commission priced him out of a move.
Juventus are still keen to sell, with PSG now the favourites to sign him before the French transfer window shits on September 2.
Previous reports have claimed the Ligue 1 champions are ready to offer Dybala a huge £11million-per-year deal to persuade him to ditch Turin for Paris.
And his representatives are now eagerly awaiting the call from PSG, according to Inside Futbol .
The report says PSG have been “sending out strong signals” that they are ready to make contact over what could be one of the biggest transfers of the summer.
They are said to be keen to sign Dybala as a replacement for Neymar Jr, who is being strongly linked with a return to his former club Barcelona .
PSG sporting director Leonardo is rumoured to have contacted Dybala personally and suggested he would be the ideal replacement for the Brazilian.
Juventus want around £80 million for Dybala, but are desperate to sign a replacement before the Italian transfer deadline on August 18.
Bayern Munich and Inter Milan have also been cited as possible destinations for Dybala, should he not move to PSG.
The star scuppered a deal to both United and Tottenham because of a haggle over image rights.
Juventus had identified United’s Romelu Lukaku as a target, but missed out on his signature after the Belgian moved to the Bianconeri’s Serie A rivals Inter Milan.
Lukaku completed a £73 million move on deadline day after relations became strained at his former club.