The Portuguese was recently jeered by the Madrid faithful following his decision to drop club icon Iker Casillas from the starting XI, and the 49-year-old's future at the club appears to now be in doubt.
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"Mourinho is still Real Madrid's coach and he remains under contract here. I think that he will stay at Madrid," Higuain said at a press conference.
"Everybody's united at Madrid. We all support Mourinho and he backs the team, too."
The Argentine attacker then went on to dismiss reports that he could leave the club himself and stressed his determination to hit top form again after returning from injury.
"I ignore all the rumours about my future. I am completely focused on Real Madrid," he insisted.
"I hope to start scoring again as soon as possible, but the most important thing for me is to feel physically well again."
Higuain has netted seven goals in 11 Liga appearances this term.