Mourinho, whose Real Madrid side open their Champions League campaign against City on Tuesday night, compared the investment made by Sheikh Mansour bin Zayed al-Nahyan since he bought the club in 2008 to that of Roman Abramovich at the Portuguese's old club Chelsea.
He said: "I don't think it is very different to Chelsea.
"Since Roman bought the club, (Claudio) Ranieri was the first coach, then I came and we won the first league, some cups and some more titles.
"Carlo (Ancelotti) then came and they continued to win and finally they won the Champions League.
"With City it started off with Mark Hughes, they started spending money and buying good players.
"Then Roberto (Mancini) came and he has done a very good job. He has created a great squad, the first cup then the first title arrived.
"I don't know if it is this season or next season with Roberto, or with another person in the future, but normally in the direction the club is going, sooner or later they will win the big cup."
Real have started their own domestic campaign poorly, winning just once in their first four league matches, but Mourinho insists he will not make wholesale changes despite questioning some of his players' commitment after Saturday's 1-0 defeat to Sevilla.
"The line-up will not be very different, nor will I try to show any player that they are not in the best condition," he said. "It will be the best that I consider to play against an opposition full of players of the highest level.
"I don't believe I have created doubts. The principal person responsible is me. When my teams win, we win together, and when we lose, I am the one responsible."
One person who is hoping Mourinho's prediction for City comes true and soon is Citizens boss Mancini.
City begin their second successive season in the continent's elite competition as the English champions having continued their remarkable recent progress by winning the Barclays Premier League last May.
That came after FA Cup success in 2011 brought the club a first trophy in 35 years but while Europe might seem the next logical target, Mancini is setting no bold targets for this particular season.
Speaking at the Bernabeu ahead of the mouth-watering Group D opener, Mancini said: "If you drive a Ferrari you can win, if you drive a Fiat Cinquecento, probably not.
"In the past we have been working for this. I think we beat good teams but we have played together for two years and we needed time.
"I am sure we will arrive to win this trophy in the future. I do not know when, but I am sure because we are working for this.
"If we want to improve every year it is possible."
City failed to progress beyond the group stages last season having been given a tough draw against Bayern Munich, Napoli and Villarreal.
This year the assignment is even tougher with the champions of Holland and Germany, Ajax and Borussia Dortmund respectively, also lying in wait as well as nine-time European champions Real.
Mancini said: "I think it was a good experience last year - we did well in the group but it was not enough.
"I think the group will be stronger this year but it will be difficult for all the teams.
"I think it is important now that we go to the second stage. After February anything can happen, but now it is difficult to say what we can do."