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Kolarov joined City last month for £16 million as part of the breathtaking spending spree which has seen Sheikh Mansour, the Premier League club's wealthy owner, spend more than 130 million pounds on the north-west English side.
Former Chelsea boss Mourinho, who joined Madrid after leading Inter Milan to a domestic and European treble last season, said even a club the size of Real could not compete with City's cheque book.
"I understand that if someone wants to compete with them for a player it is very difficult, they are dominant in the market," Mourinho told Sky Sports.
"The player they say they want is the player they get," the Portuguese added. I was interested in Kolarov when I came here but I couldn't compete with them as they went to values that I couldn't.
"If they have the money they can do it, if they have the ambition to win the Premier League they can do it." Mourinho also ruled out the possibility of Real signing either Chelsea striker Didier Drogba or City's Emmanuel Adebayor.
Asked about luring Adebayor to the Bernabeu, he said: "I think no chance.
"The historical dimension of Real Madrid and Manchester City you can't compare. But the economical dimension you can compare.
"And maybe they will win (the Premier League).
"So I think at the minute Man City is the club to keep their best players and to buy the players that nobody expects them to buy.
"I don't think, just one year after buying Emmanuel from Arsenal, he's the player to leave." As for Drogba rejoining his former boss, Mourinho said: "Again, no chance."
Mourinho believes this season's Premier League title race is between City, Manchester United and defending champions Chelsea.
"I believe Chelsea, Man United and Man City, that's it," he said, making it clear Liverpool were out of title contention.
"It's very difficult for (new Liverpool manager) Roy Hodgson as over the last three years they have been getting worse, worse and worse.
"He needs time."
