The Argentina striker continues see off all comers this season as he establishes himself as the club's No1 goal scorer.
"It would be nice to end my career here. Madrid and the city is my second home. It would be great. I would like Madrid fans to remember me as a great person, humble and hard working," said Higuain.
"For 2010, I want to win the Champions League with Madrid. In addition, the World Cup with Argentina."