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Morata has also been touted as a target for Juventus’ rivals AC Milan, now backed by wealthy Chinese investors.
Where Morata’s future lies is likely to be determined by Chelsea’s next manager, with Conte expected to be sacked.
However, former Chelsea and Milan striker Hernan Crespo recently advised Morata to stay put this summer.
"I think he is a great player," said Crespo. "He is a young player who has a lot of trophies already. However, you need to be patient.
"He has showed he is a very good striker, but normally when you play in a big team it is difficult to be at a high level for the whole year. In the past, the same thing happened at Juventus, but that is because he is young.
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"He can be the future of Chelsea but it depends on him. It is important to see if he is happy. If he is happy at Chelsea and he can show his best in this team then it would be great for everyone, but if he wants to come back to Juventus and make another experience then we will see.
"It is different than my experience at Chelsea because I was older than him. I had already been past my best level. The Premier League at that time wasn’t the best in the world. Now it is. At that time, when I played, Serie A was actually the best. Then, AC Milan called me, the second time was Inter [Milan].
"It was difficult for me to adapt that way around. If you want me to offer my personal opinion, I say stay at Chelsea! Show your best there because you play in the best league in the world. Chelsea can win the league again. They have big decisions to make, to go with Conte or not.
"For the players, though, everything is clear for their futures, it is down to them to choose. I think he should stay and that’s regardless of the manager, but you never know, whoever the manager is may have other ideas."