Mourinho told Spanish daily ABC that Argentina forward Higuain, reportedly a target of several clubs including Paris St Germain and Chelsea, would remain to compete for a starting place with Karim Benzema next term.
"He has an excellent contract for many years," said Mourinho, whose side wrapped up the club's first La Liga title in four years on Wednesday.
"He is not one of those players who arrived a year ago and earns little, he earns at the same level as others," he added.
"An offer of 40, 50, 60 million euros could be made, whatever, but Madrid will not want to sell. I don't have a problem. My two centre forwards for next season will be Higuain and Benzema."
Mourinho said Spaniard Adan, a youth academy graduate who is second choice to Iker Casillas and made only five appearances in all competitions this season, had told him he was thinking of leaving to get more playing time, an ambition he said he admired.
"If Madrid is combing the market for a goalkeeper it's because Adan does not want to stay," Mourinho said.
"My job is to convince Antonio to stay and I have asked Iker to help. Adan is the second-choice keeper and if we cannot convince him to stay we'll have to find a solution."