Real are understood to be chasing a number of attacking targets this summer, casting doubt over the future of those already at the club.
Higuain is confident he remains part of Jose Mourinho's plans, though, and hopes he can play a leading role in their pursuit of major honours.
"My wish is to stay with Real Madrid," he told AS.
"I feel very loved by the fans and I want to win many more trophies with this club. There's nothing better than playing at one of the world's biggest clubs.
"I am very happy at Real Madrid.
"It is clear that you have to work very hard to become and remain a first-team regular at a big club like this. There's always a lot of competition for places.
"I am pleased to have the chance to play with the big stars here and want to continue winning things."