The 27-year-old has endured a frustrating campaign in Turin, with just 10 starts and six substitute appearances in all competitions.
With Juve officials keen to strengthen their financial position, speculation suggests that the Argentina international could be allowed to leave in the summer.
According to France Football via Mail, the Blues and Spurs are both monitoring the situation ahead of a possible bid during the summer.
The report goes on to claim that the Premier League duo may be prepared to pay as much as €55m for the Argentine.
Dybala is contracted to Juventus until 2022.