Mourinho was one of the names tipped to replace Sir Alex Ferguson at Old Trafford, but when the legendary Scot decided to retire at the end of last season he quickly announced that Moyes was his choice to fill the hot-seat.
Moyes has come under pressure in his first year at the helm after a miserable defence of their Premier League crown, and United's final chance of silverware this term lies in the Champions League after making it through to a quarter-final against Bayern Munich.
Mourinho believes Moyes needs to be given time to adjust to a new club, and has dismissed suggestions that he ever had an interest in the United role.
"I don't know if Sir Alex thought of me for United or not," Mourinho said in The Sun.
"The point is he clearly knew I wanted to go to Chelsea. I spoke with him after we (Real Madrid) knocked United out of the Champions League last season and I told him what I wanted to do - that Chelsea is what I wanted, that was the direction I wanted to go."
"As for David, he went to a new club - a club with a new reality for him - and he is adapting.
"Next season will be better and attention, attention! He can still win the Champions League this season."
Asked if Moyes would have been sacked by now if he had been at Chelsea, Mourinho added: "Maybe not. Maybe Chelsea now has a different vision, working to a different profile with a different strategy."
Mourinho is fighting for the title with Chelsea and determined to become champions, although he is already proud of what has been achieved at Stamford Bridge this season.
He said: "We know every match is vital until the end of the season. We don't give up, we don't give in - we go to win every game.
"This is a special season for me and my Chelsea even if we don't win anything. To push to win the Premier League and to go from the Europa League to the last eight of the Champions League is an important step."
Liverpool are among Chelsea's main rivals for the title and Mourinho is happy that Brendan Rodgers, a former coach at Stamford Bridge, is enjoying success.
He said: "We are friends. If I made any contribution for him to become a manager at a big team then I'm happy with that."