The 19-year-old right-back completed his £19m switch from Porto earlier this month despite being on crutches, having picked up a knee injury towards the end of last season.
Dalot has been told to take things easy by his new employers but the Red Devils have learned the teenager is now hopeful he will be able to play some part in United's pre-season tour of America later next month.
That will come as a welcome surprise to Jose Mourinho, who has tipped the youngster to make a big impression at Old Trafford, having kept his pursuit firmly under the radar.
It's understood United's recently revamped conditioning team will take a look at Dalot in the next ten days and are planning a special programme to help bring him further up to speed.
Dalot is sorting out a place to live in Manchester and he has spoken further with Mourinho on the telephone, although United insiders insist the club's own medical staff will have the final say on when he can take part again in competitive action.