Real are reportedly chasing Tottenham Hotspur's Croatian playmaker Luka Modric, with one or both of midfielders Kaka and Nuri Sahin expected to move on after disappointing stints in the Spanish capital.
"We are hard at work preparing because we are well aware of the fact that it is not going to be easy, quite the contrary," Mourinho told Fox in an interview during Real's pre-season tour of the United States.
"The team is almost complete," added the Portuguese, who helped end Barcelona's three-year grip on the La Liga title last season.
"They are special players, we have a lot of the best players in the world and my team's motivation when faced with new challenges never ceases to surprise me."
Modric refused to take part in Tottenham's tour of America and manager Andre Villas-Boas said he would be fined as a result.
The 26-year-old has four years left on his current deal at the North London club and carries a price tag of around £40 million.
Real defender Sergio Ramos, one of the club captains, said there was still room to add to the squad before the transfer window closes at the end of this month and that Modric would be a good fit for the team.
"There haven't been many departures or signings, but we are open to everything," Ramos told a news conference in Los Angeles.
"We've got a great squad, with amazing footballers, and one or two more will join," added the Spain international.
"I like football and good footballers and Modric is one of them. He currently doesn't play in this team and I can't say any more than that. If he joins he'll bring something to the team."
