Ibrahimovic, the Barcelona striker who endured a patchy first season at the Nou Camp, played for Mourinho at Inter Milan between 2008 and 2009.
"Mourinho is one of the best coaches in the world," Ibrahimovic told reporters on Thursday, ahead of Barcelona's pre-season friendly against Norwegian side Valerenga.
"When he comes to a new club he will build it up to be a winning machine. It will be difficult to beat (Real), but we are the best team in the world."
Barcelona won the Spanish league in 2009 and 2010, and the Champions League in 2009.
Ibrahimovic, the Sweden international who scored 16 goals in his first season at Barcelona, said he expects to improve in his second, and that the arrival of David Villa should not put his place under threat.
He admitted he had discussed his situation with coach Pep Guardiola after Barcelona bought Villa, Spain's top scorer at the World Cup, from Valencia.
"Every time I change clubs, I think the first year is always the (most) difficult one, and from all the clubs that I've played in, my best first year has been in Barcelona," Ibrahimovic said.
"He (Guardiola) says I'm important, and then I take it as I will play. If you're not important, you don't play."
Ibrahimovic said Villa was one of the world's best players who would help Barcelona next season. "With Villa on the team we will be even stronger and have even better chance to win the Champions League," he said.
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