The Brazilian midfielder arrived from Shakhtar Donetsk in the summer for over £50million.
And he was wanted by Manchester City since January, but chose the Red Devils instead.
"That's true, I received an offer from them [City] and even talked to my Brazilian team-mates who play for our neighbours," said Fred, in an interview with FourFourTwo.
"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."