According to Goal's Romeo Agresti, the Blues forward was photographed in Milan meeting with his agent, Juanma Lopez, and Paratici, while his Italian agent, Beppe Bozzo, has also recently met with alternative suitors AC Milan.
Morata, 25, only moved to Stamford Bridge last summer from Real Madrid in a deal worth £60 million.
He hit the ground running in the Premier League, netting six goals in his first six appearances in the English top flight.
However, he subsequently scored only five more goals in a further 25 appearances and increasingly played a backseat role to Eden Hazard and January signing Olivier Giroud.
Morata's recent omission from the Spain squad for the 2018 FIFA World Cup was just the latest in a long run of disappointments for him in 2017-18.
It would be no surprise were Morata attracted by the prospect of a return to Juve, where he thrived in a two-season spell from 2014.
Per Agresti, even if Chelsea are open to selling him they will want to make a profit, meaning Juve will need to shell out more than £60 million to snap him up.
Given the Italian champions already boast a forward line that includes Gonzalo Higuain, Paulo Dybala and Mario Mandzukic, it seems an unlikely transfer.
Milan, though, are lacking a prolific goalscorer and may be open to spending big for Morata if they feel he will be able to help them break back into the top four in Serie A.