Conte was in charge of Juventus when he convinced Morata to join the club from Real Madrid, although he ended up leaving to take charge of the Italy national team before the Spain international arrived in Turin later that summer.
Morata stayed two seasons at Juve before Madrid activated a buy-back clause in his contract last summer amid interest from Conte - now at Chelsea - and a host of other clubs.
Standard Sport understands that Conte remains keen on bringing Morata to Stamford Bridge this summer as he looks to bolster his options up front.
And Morata - who has spent the season being used mostly as a substitute by Real manager Zinedine Zidane - has admitted he would love to play for Conte because of the belief he showed when he oversaw his move to Juventus three years ago.
"Conte is the manager who most 'bet' on me, without even ever having had me in his team," Morata told The Guardian.
"I am very conscious of that: he bet on me for Juventus, but left before I arrived; then he wanted me at Chelsea come what may. He knows me better than I could imagine, I am sure, and that is important: it motivates you to work hard, train well.
"I feel indebted to him because he is the coach that most trusted in me, most wanted me, who made me feel I could perform at the highest level. And yet I have never had the fortune to actually work with him. I am sure sooner or later I will.
"The future excites me, whether that is Madrid or somewhere else. I still have to learn, improve. I can do a lot but I need to play more and for someone to really back me. Either I take off or I end up in a position of comfort, playing games occasionally."
He added: "I am no longer the youngest, I am 24, it is a big moment."