The 24-year-old has been struggling to break into the starting XI at the Santiago Bernabeu, though, with head coach Zinedine Zidane preferring Karim Benzema up front.
Morata's situation at Madrid has not gone unnoticed elsewhere and recent reports suggest Chelsea are ready to make another move for the striker come June and he is relishing the prospect of potentially linking up with Conte.
"Various Premier League coaches called to tell me to play for them. I said yes, I would like to, that if I had to leave I would almost certainly go to London, but that I did not know what Madrid would do," Morata told The Guardian.
"I knew they would bring me back, but I did not know if it was to keep me or sell me. Madrid said they did not want to sell, so here I am. I am very happy at Madrid and they support me, but if an offer like that came again and they want to sell, I should not close doors. I loved Italy, but if one day I have to leave, I am sure it will be to the Premier League.
"I spoke directly to [Tottenham boss] Mauricio Pochettino and Antonio Conte, although the norm is clubs call my dad or agent. I remember talking to my dad then and him saying that Conte was going to win the league with Chelsea.
"Conte is the manager who most 'bet' on me, without even ever having had me in his team. 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.
"I am no longer the youngest, I am 24, it is a big moment."