The Spain international found himself at the centre of a tug of war between the Red Devils and the Blues during the transfer window with Jose Mourinho thought to be on course to land the Real Madrid striker before the Premier League champions swooped in.
In the end, United switched their attention to Romelu Lukaku, landing him for £75million from Everton, while Morata chose to go to Stamford Bridge for a similar fee.
The 24-year-old says he had lots of offers to consider but was set on west London once he had spoken to Conte, who he had previously worked with while on loan at Juventus.
"I had various offers this summer, not only Chelsea and Manchester United but also from different leagues," he told the Daily Mail. "It was a good situation for me.
"The most important and best conversation I had was with (Antonio) Conte, he wanted me to come here.
"At the start of the summer, I didn't know that Chelsea were interested in me. I thought they were in for a different player, maybe Lukaku or maybe someone else, I don't know. I didn't think the option of Chelsea was open.
"But I spoke with Conte several times - and not only this summer. I felt in debt to him.