Dybala, 28, is a free agent after leaving the Serie A giants at the end of last season following the expiry of his contract.
The Argentina international is currently searching for a new club, with reports suggesting his preference is to continue playing in Italy, despite awaiting offers from abroad.
According to Corriere dello Sport, they claim Dybala's exceedingly high demands have put off several clubs interested in him.
However, according to the Italian newspaper, the player is set to take a significant pay cut in order to facilitate a move to a European club, with Roma one of the teams interested.
Mourinho is evaluating the former Manchester United and Tottenham transfer target's situation, but his side must offload several players if they are to sign him.
Amadou Diawara, Gonzalo Villar and Justin Kluivert could all make way to help draft in the former Juventus star.
According to Sky Sport in Italy, Napoli are also in the hunt for Dybala, alongside Roma and both have been in advanced talks with the representatives of the player.
Napoli, however, are facing the issue of image rights which is preventing them from making an official bid for Dybala.
Former Roma star Zbigniew Boniek has insisted the Argentinian star would be a 'fantastic' addition at the Stadio Olimpico.
Boniek, a former Roma and Juventus star, believes he should join the Giallorossi.
"It would be fantastic for him and for Roma," he wrote on Twitter while on holiday in Italy.
Dybala joined Juventus for €40million (£33.8million) in 2015 and scored 115 goals in 293 appearances with the Bianconeri.
He has 98 goals in 271 Serie A appearances with Juventus and Palermo, and looks to remain in Serie A ahead of the new season.