The Portuguese told a news conference on Friday he had known his fellow countryman since he was a youngster and that he was proud to see "his evolution as a person".
"I'm very proud that a good friend like him reaches this level," said Mourinho on the eve of Premier League leaders Chelsea's home game with Burnley. "I've known him since he was a kid.
"He can win or lose the election but one thing he has won already is credibility. He has won credibility by the campaign he has run, a polite clean campaign."
Figo entered the race to become president of world football's governing body last month, saying he would run against incumbent Sepp Blatter at the election in May because "football deserves better" than its existing reputation.
The former Portugal playmaker, 42, also wants more of FIFA's income spent on grassroots development.
Figo is one of three men challenging Sepp Blatter. Michael van Praag, president of the Dutch FA, and Prince Ali Bin Al Hussein of Jordan, a member of FIFA's executive committee, are also standing.
(Writing by Tony Jimenez, reporting by Clare Lovell, editing by Pritha Sarkar)
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