The youngster has struggled for game time since Ole Gunnar Solskjaer took over as manager.
Injuries and a lack of form have meant the Portuguese has slipped down the pecking order at Old Trafford.
And the Mirror says the 21-year-old has impressed Carlo Ancelotti.
The Everton manager wants to make a move this summer, and the player would likely cost in the region of £10 million.
Dalot would be a long term replacement for Seamus Coleman, and would be eased into first team duties in the coming season.