The Serie A side are interested in Morata and the club's general manager, Beppe Marotta, has twice spoken about the player that the champions-elect lost two years ago, as Real Madrid activated their €32 million ($38m) buy-back clause.
Chelsea went on to buy Morata for £60m ($81m) the following summer, but he has struggled to make the impact many predicted this season.
In interview with Marca, the 25-year-old revealed that his season has been impacted by a painful back injury.
It is expected that he will start in Chelsea's upcoming match against Huddersfield as he comes back from injury, and manager Antonio Conte hinted ahead of the game that he thinks Morata will stay at Chelsea.
However, Juventus could yet increase their efforts in the summer when the manager situations are resolved at both clubs, with both Conte and Juventus boss Massimiliano Allegri rumoured to be on their way out.
It is very unlikely that Chelsea would let Morata go for any less than what they bought him for in the summer, with a feeling around the club that he will improve next season.
Morata is known to have enjoyed his time in Turin both on and off the pitch, as he met his wife Alice while winning a host of honours with the Italian giants.
The 25-year-old has recently lost his place to Olivier Giroud, who has been in good form since joining from Arsenal for £18m ($24m).
This situation may lead to him being dropped from the Spain squad for the World Cup, despite playing a huge role in their qualification campaign.