Having re-signed for the Blues while Mourinho was still at the helm, the 29-year-old became a pivotal player as Chelsea won their 4th Premier League title in 2014.
The Red Devils finished in sixth place in the Premier League table last season but still got their hands on the EFL Cup and the Europa League.
Conte added that he was optimistic Morata, who Chelsea signed for a club record £70m, has a bright future ahead of him at Stamford Bridge.
The Italian told Sky Sports: 'Matic knows very well what I think about him.
"There's responsibility on Bakayoko not just to bring the talents that he has - and he has many - but also the discipline to fit into the system".
Sa nièce se filme en train de mettre son bébé au frigo
Mais pour la mère, une chose est sûre: "Je ne laisserai plus jamais mon enfant avec ma nièce et ses amies, de toute ma vie". A son retour, elle ne s'est doutée de rien car les jeunes filles s'étaient (heureusement) empressées de reprendre l'enfant.
But Lampard believes the 24-year-old's determination to force his way out of a comfortable situation in the Spanish capital is a good sign.
The 23-year-old is not the finished article, but his energy and physical presence make his flawless for the Premier League. It's a very tough league and he'll have to stand up to that.
He's available, can we get him?' I think Chelsea more often than not have backed their managers and brought in the players needed. You would applaud that but those players aren't even at the club now.
"You saw that with Chelsea last year - him and Kante were magnificent last year and that allowed Hazard, Fabregas, whoever else was playing that bit of freedom, and I'm hoping he'll do that for United - a bit of freedom for Pogba, Martial, Lingard, Mkhitaryan - these players really need to step up this year".
"I heard whispers at the back end of last season that he wanted to go and even if the club can not come out and say too much about that, maybe there was an element of that in play here when this deal went through. Hopefully by the time the window shuts it all comes together, and then the club moves forward".
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