The Portuguese boss labelled himself the ‘Special One’ during his time in charge of Chelsea between 2004-07, when he won back-to-back Premier League titles with the Blues.
But Mourinho feels he deserves a new status after becoming the first manager in history to win the title across Europe’s top three leagues.
“I’m the only one to have won the three biggest championships in the world,” he said in an interview on Portuguese television channel Sic.
“So whether it pleases or not, if one recognises my value or not… people should maybe call me ‘unique’ rather than ‘special’ until someone else wins three championships like me.”
The Portuguese coach joined Real Madrid in 2010 and won the Primera Liga title in his second season to become one of the few coaches to win titles in four different countries – Portugal, England, Italy and Spain.
He is also the only coach to have won two UEFA Champions League titles with two different clubs, with FC Porto in 2004 and Inter Milan in 2010.
The 49-year-old said he felt “an enormous joy at Inter Milan” when they won their titles but says his ambitions are changing with age.
“I’m turning increasingly towards people,” he said. “That’s what motivates me more and more, instead of pursuing individual goals.”