The Brazilian moved to Old Trafford from Shakhtar Donetsk in a £52million deal in June.
He admits he held talks with City but revealed the lure of working alongside Mourinho was too good to turn down.
“That’s true, I received an offer from them (City) and even talked to my Brazilian team-mates who play for our neighbours,” he told Four Four Two magazine.
“They were trying to convince me to join them, but in the end it didn’t happen.
“Then it was the summer and, as I said, there were other offers, including from United. I quickly decided that was the right move for me.
“Mourinho is a top, top professional and every player likes to work with such a winner. I’m learning things from him, that’s for sure.
“He can be quite strict, but that’s part of his job.
“He’s also friendly and funny off the pitch, and jokes with us in the dressing room.
“Jose was crucial in my decision to join Manchester United and I’m grateful for his interest in my football.”
The 25-year-old is currently preparing to face the club he rejected in ten Manchester derby at the Etihad on Sunday.
He has started the last two Premier League games – victories over Everton and Bournemouth – after losing his place in the side following a 3-1 defeat by West Ham at the end of September.
Although Fred did not play any part in the 2-1 win against Juventus in the Champions League on Tuesday night, he could come back into the side to face City as there are doubts concerning Paul Pogba’s fitness.
He sat out Friday’s training session because of what is being described as a ‘little injury’.
Meanwhile, Romelu Lukaku completed a full session as he recovers from injury and Alexis Sanchez took part after picking up a knock in Turin.
Mourinho has promised fans he will not park the bus against their free-scoring neighbours as they look to close the gap on the top four.
Seventh-placed United are four points behind Tottenham in fourth and a further five off leaders City.
“We are going to try (and win),” the United boss said.
“I cannot say we are going to be successful in our motivations, in our desire, but we played two difficult matches away against two very good teams, Chelsea and Juventus, and we managed to get good results.
“Even if the good results were not in our pockets, the performances were there, the positive attitude was there.
“So we are going to try but City are a very powerful team.
“If we draw the gap is still nine points, if we lose it’s 12, so I don’t think that is the way to look at the match.
“We have to just think about the match, is difficult enough as an isolated event, if you want to put that match into the context of where we are and where we can be.
“I want to play it as an isolated match, a difficult match against a difficult team, but they will also think it’s a difficult match for them.”