The 23-year-old defender has played in all but one of United’s Premier League games this season, as an unbeaten start has left them second in the table.
And Bailly has revealed that Mourinho has helped him develop as a player and given him the motivation to build on last year.
He said: “For me, the aspect that was very important and where I see improvements - and can improve even more, to be honest - is the tactics, as well as the high level of concentration that’s required.
“For a young defender it’s very important and with this manager I’m positive about the future.
“It’s not so much that it helps as that it motivates.
“Winning a trophy is very important and I think that, with the trophies we’ve won, it’s a huge motivation to win even more.
"It’s what we always have in mind: to have the desire, the aim to win several trophies because it’s a good thing for a player’s career."
Bailly signed for United last summer for £30m and the Ivorian enjoyed a successful season, helping them win the Community Shield, the EFL Cup and the Europa League.
He has developed a strong partnership with Phil Jones this season in the heart of a United defence that has only conceded two Premier League goals.
They return to league action after the international break against Liverpool at Anfield.
