The Portuguese boss made Bailly his first signing at Old Trafford in the summer when he paid Villarreal almost £30m for the centre-back.
Even though Bailly has been fighting an injury, he will be unavailable for almost four weeks as he was named in the Ivory Coast squad for the Africa Cup of Nations.
Speaking about Mourinho, Bailly claims he has already helped him become a better player.
“He’s a great manager, the best in the world,” he said.
“It is a pleasure to work and learn with him. 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.”
He’s been an indispensable member of the squad and would have been a massive blow for United, had Mourinho not taken charge of his makeshift defence, leading his men to 11 unbeaten fixtures.
Hopes are Bailly can keep himself fit as he’ll be looking to slot right back into the starting XI as soon as he’s done at the Africa Cup of Nations.