The Argentina international has enjoyed a productive campaign for the Italian giants, contributing 11 goals and four assists from his 23 appearances in all competitions.
However, the 28-year-old has less than six months remaining on his contract, putting him in a position where he can hold discussions with foreign clubs.
According to Sportitalia, Liverpool are monitoring the situation, even though a stay in Serie A looks the most likely outcome.
Juventus are yet to follow through with their offer of a new deal, while Inter Milan are known to be ready to pounce if it becomes apparent that Dybala wants a new challenge.
The playmaker, who is in his seventh campaign in Turin, has won 12 pieces of silverware during his time at the club.