Soon after the end of the season, United spent around £19m in order to sign Dalot from Porto, and the youngster is expected to rival Antonio Valencia for a place at right-back.
However, Mourinho has confirmed that Dalot is still recovering from a knee injury, despite being taken on the club's pre-season tour of the United States.
The 55-year-old is quoted by Sky Sports News as saying: "Dalot is injured; we knew that but we didn't want to lose him because of that.
"He is recovering really well. We think he can start training with the team when we go back to England. He will not be ready for the start of the season but we think he'll be ready for September."
Dalot sustained the injury shortly before the end of last season having made seven first-team appearances.