Dybala, signed last summer from Palermo for 40m euros, has quickly become a fans' favourite in Turin as the champions continue their fightback following a disastrous start to the campaign.
In 19 league appearances, the Argentinian has struck 11 goals including some spectacular efforts that have attracted the attention of La Liga giants Barcelona and Real Madrid.
A report in Turin-based newspaper Tuttosport claims Juventus president Beppe Marotta rejected an offer of 80m euros for the player when Barcelona sporting director Ariedo Braida knocked on the door in December.
It added that Barcelona returned with an improved offer in recent days, which the Italian champions also knocked back.
Barcelona and Real Madrid are among the top European clubs reportedly eyeing the 22-year-old, who is known for his creative skills, dribbling and keen eye for goal.
If the report is confirmed, it would put Dybala among Barcelona's most highly-rated players, alongside Brazil striker Neymar, who it is estimated cost the club at least 83.4m euros in 2013.
Uruguayan Luis Suarez cost the European champions around 95m euros when he joined from Liverpool in 2014.
It would also underline Juve's intention to hold on to a player they made great efforts to acquire, securing his signature on a five-year deal shortly after Dybala hit 10 league goals for Palermo prior to Christmas last season.
Juventus won their first league and Cup double in 20 years last season, when coach Massimiliano Allegri also steered them to the final of the Champions League, and an eventual 3-1 defeat to Barcelona.
Allegri's men sit second in Serie A, two points behind leaders Napoli before hosting Roma on Sunday