The Spanish striker tells Goal that his Juventus team-mate trains twice as hard as everyone else and says he can have the pick of Europe's top sides if he decides to leave Turin
Having set up Juventus' second goal with a brilliant solo run, Morata was substituted after 72 minutes against Bayern Munich in the Champions League last-16 second leg last week.
His exit coincided with a dramatic change on the scoresheet, with Juventus 2-0 up at the time of his withdrawal but eventual 4-2 losers after extra time.
"We were winning 2-0 and we ended up losing 4-2," Morata reflected. "It's very difficult to understand and to digest, but the Champions League and football are like that.
"[Massimiliano] Allegri hasn't spoken to me about the change, but I imagine he wanted to win as well. And I'm sure he decided to take me off in that moment so that we could defend or in order to make a tactical variation."
So Morata, a Champions League winner with Real Madrid in 2013-14 and a finalist with Juventus last season, will not be present in this season's showpiece at San Siro on May 28.
However, he believes winning Serie A and the Coppa Italia would represent a successful campaign for the Bianconeri.
"We have the final of the Coppa [against AC Milan] and we are leaders of Serie A," he said. "When you are used to winning and you are the best in Italy, sometimes you see it as insufficient.
"But I think that, to win the double two years running, and especially after our horrendous start to the season, I think that would have a lot of merit.
"When you have won so many titles in Italy, you have to aim high. But honestly, I think that if we hadn't lost against Bayern, Juve would have been very dangerous in the Champions League.
"Last year there were 10 minutes in which the whole of Europe saw that we could have been champions of Europe. That's football. In the end we lost against Barcelona, but this would be a great season if we could win the league and the cup."
- Goal