The defender joined United from Porto last month on a five-year deal for a fee of around 19million.
Dalot had injured his knee at the end of the Porto season, and has been recovering with the help of crutches.
He did however travel to the USA with the team, despite being unable to play.
'Sky Sports' reported that Mourinho was happy with his progress. He told them:
"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."