The 46-year-old is now out of work since resigning as manager of Los Blancos in May just five days after winning his third consecutive Champions League trophy.
Mourinho is entering his third season in the Old Trafford hotseat but the campaign follows a tumultuous pre-season in which the manager regularly complained about missing out on transfer targets.
The 46-year-old also won La Liga with Madrid in 2017, as well as two Club World Cup trophies during his two-and-a-half years in charge at the Santiago Bernabeu.
Liverpool manager Klopp: Why are we Man City's only challengers?
Jürgen Klopp was pleased with Liverpool's convincing start to the season, but has warned there will be much tougher tests ahead. Everyone knows the Reds' front three are a sight to behold when they are in full flight - and they were at it again here.
The United boss has been in the media for all the wrong reasons throughout the summer, complaining about transfers, players, and his relationship with United's executive vice-president, Ed Woodward.
Dalot moved to United in a £19m deal from FC Porto earlier in the summer but arrived carrying a knee injury that he sustained while playing in Portugal during the latter stages of last season.
He has previously played for Real Colorado as part of the USA soccer development academy and was earmarked for a place in United's U18s squad this season after impressing on trial last season.