Bailly, 22, arrived at Old Trafford from Villarreal in June in a deal reportedly worth £30million.
The Ivory Coast international was full of praise for Mourinho, whose team are sixth in the Premier League.
“He’s a great manager, the best in the world, it is a pleasure to work and learn with him,” Bailly said.
“I hope it continues like this and that I stay at United for a long time.
“I’m truly happy, with my team and my team-mates. Bit by bit, I’m getting to know more.”
Bailly has made 11 league appearances for United this season, settling in well in England.
He compared the Premier League to LaLiga, where he spent the previous two seasons, and said there were major differences.
“From what I see, football in Spain, they also have a great league,” Bailly said.
“LaLiga is the best in the world, but here it is different, very direct, there is more contact and more strength.
“And like I said, little by little, and with more training under this manager, I hope to improve. Manchester is a nice place, I’m happy here.”
