Morata began life at Stamford Bridge in prolific fashion after his move from Real Madrid last summer, scoring six goals in his first six appearances, but has struggled to maintain his form.
The January arrival of Olivier Giroud brought fresh competition for the Spaniard which has saw him reduced to the bench on five occasions.
The Independent has reported that Massimiliano Allegri would be interested in offering Morata a route out of west London with a return to Turin.
Morata spent two seasons in Serie A with Juve, scoring 27 goals in 93 matches in all competitions.
Nonetheless, Allegri, who has committed to another season with the Italian champions despite interest from Chelsea, is looking to improve his squad as he looks to mount another challenge for Champions League glory next season.
Juve could take advantage of an uncertain period for Chelsea, who are likely to be on the lookout for a new manager with Antonio Conte set to depart.
Reports in Italy, however, suggest that any move for Morata would be temporary in the form of a financed loan, similar to that of Juan Cuadrado’s two-year temporary spell at Juve before making his switch from Chelsea permanent in 2017.
It is, however, a deal that might not fly with Chelsea this time round given the amount they paid for the 25-year-old last summer. Morata signed a five-year deal with Chelsea worth £7 0million.