Corriere dello Sport says Juve are ready to pay around £13m for two-year loan.
The contract would also include a compulsory £40m purchase option.
The Spaniard only arrived at Stamford Bridge 12 months ago. But since swapping Real Madrid for west London, Morata has underwhelmed.
The striker was snapped in Milan with his agent yesterday - also present was Juventus director of sport Fabio Paratici.