Higuain, 22, netted three clinical goals to fire Real to a 4-1 win that lifted them back above champions Barcelona to the top of La Liga and Valdano said the club were in talks about extending his current contract which ends in 2013.
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"We don't just want him to renew his contract but we want him to see out his career at the club," Valdano, a former Real Madrid and Argentina player, said in a television interview.
Higuain was accused of selfish play after Real were knocked out of the Champions League by Olympique Lyon on Wednesday, but Valdano defended his compatriot and said his response on Sunday had been "tremendous".
Real's Portuguese forward Cristiano Ronaldo was twice in promising goal-scoring positions against the French side at the Bernabeu but Higuain opted to go it alone both times and the chances went begging.
"All the comments this week about someone who is a great forward and voracious in front of goal seem to me unjust," Valdano said. "You can't condemn him for one passage of play during three otherwise immaculate years."
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