Conte brought Morata to Juventus from Real Madrid in 2014.
But the Chelsea boss left the club as soon as the Spanish striker arrived to take over the Italian national team.
Morata rejoined Madrid last summer after the La Liga giants activated a £23million buyout clause.
Real Madrid star Alvaro Morata expects to work with Chelsea boss Antonio Conte
But he has since been linked with a move away from the Bernabeu, with Chelsea reportedly keen on his signature.
And now the striker has revealed he expects to work with Blues boss Conte at some point in his career.
"Conte is the manager who most bet on me, without even ever having had me in his team," Morata told The Guardian.
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"I'm very conscious of that – he bet on me for Juventus but left before I arrived; then he wanted me at Chelsea come what may.
"I feel indebted to him because he's the coach that most trusted in me, most wanted me, who made me feel I could perform at the highest level.
"Yet I've never had the fortune to actually work with him.
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"I'm sure sooner or later I will."