Real roared to their 32nd Liga crown in 2011/12, collecting a record 100 points and finishing nine points ahead of rivals Barcelona.

And the 49-year-old Portuguese coach has warned fans their team will face stiff competition in the coming campaign, but is confident his players will soon be ready for the rigours of their title defence.

"We are preparing rigorously because we know it will not be easy, on the contrary," Mourinho said at a press conference.

"Our squad is almost complete. These are very special players, some of the world's best."

Real have long been targeting their 10th Champions League triumph, but Mourinho has urged fans to not forget his side's record-breaking title win of last season.

"There is a lot of passion when it comes to Madrid and the Champions League, but what we want is to win titles.

"In my opinion, winning the league with a record amount of points is something difficult and unique."

Real Madrid are on a promotional tour in the United States, and Mourinho took the time to reflect on the status of football in the country.

"I know the sports culture of this country, and that football will never be their first sport," he said.

"But everything surrounding football here is very positive, and the football here has great possibilities."

The league champions will begin their title defence on August 18 by welcoming Valencia to the Santiago Bernabeu.