The 21-year-old striker was ruled out for seven weeks after suffering a second grade tear of the medial collateral ligament in his left knee during his first training session after moving from Real Madrid.
With the new campaign due to get underway at the end of this month, reports suggested the Serie A champions could be tempted back into the market in the absence of Morata.
However, the Spaniard believes he could return to full training sooner than originally expected.
"My knee is getting better, I'm recovering well," he told AS TV. "In about 30 or 35 days I will be ready.
"It was a shame about the injury but I'm working with the physios to play again soon.
"Signing for Juventus has been a great joy, I'm really happy with my new team."
Morata signed a five-year deal with the Turin giants last month after the two clubs agreed a €20million fee.
