After scoring 114 goals during his seven years Juventus, the Argentina international is now a free agent after failing to agree fresh terms with the Turin-based outfit.
At one stage, it appeared that Inter Milan were on the brink of signing the 28-year-old, but a transfer to San Siro has currently failed to materialise.
Manchester United are another club who have allegedly been monitoring any developments with the playmaker's future with Erik ten Hag keen to add to his creative options.
However, an agreement does not appear to be imminent, seemingly leaving two Serie A clubs to do battle for Dybala's services.
According to Sky Italia, Roma and Napoli are both keen to strengthen their respective forward lines with the addition of Dybala.
Roma, who won the inaugural Europa Conference League in 2021-22, are looking to put together a squad capable of earning a return to the Champions League.
Meanwhile, Napoli are in the market for attack-minded players with Lorenzo Insigne and Dries Mertens having both departed the club on free transfers.
At this stage, however, it is claimed that both clubs are yet to get anywhere near to meeting Dybala's wage demands.
Inter were allegedly prepared to pay Dybala as much as €7m per year, including adds-ons, before being left with the need to make room on their wage bill.
Neither Roma or Napoli have reached a point where they are prepared to match that figure, leaving Dybala's future up in the air.
The report adds that AC Milan are in a similar position, although it remains to be seen whether Dybala will be prepared to lower his demands over the coming weeks.
During his final year with Juventus, he contributed 10 goals and five assists from his 29 appearances in Italy's top flight.