The former Napoli player ended his two-month goal-scoring drought before the winter break with the winner against SPAL, bringing his tally to six goals in 15 Serie A games -- below his rate at his previous clubs.
"A goal can change things, but if he is to continue here, he needs to take on responsibility," warned Leonardo.
"He had a tough moment, he has to put it behind him and get to work."
Milan have an option to buy Higuain who has also been linked with a possible move to join former Napoli coach Maurizio Sarri at Chelsea.
"There's no point following rumours and gossip," said Leonardo.
"He is here right now. Seeing as he is here, he needs to get down and actually do something for this team."
AC Milan have crashed out of the Europa League and dropped to fifth in Serie A.
Brazilian Leonardo also confirmed there have been no formal offers for Italian forward Fabio Borini or Croatian midfielder Alen Halilovic who have been linked to Chinese club Shenzhen and Turkish outfit Besiktas respectively.
Leonardo was speaking during the presentation of new Brazilian signing Lucas Paqueta, who arrived from Flamengo on a four-and-a-half year deal worth 35 million euros (USD 40m).
The 21-year-old could make his debut in the Italian Cup against Sampdoria on Saturday or next week's Italian Super Cup match against Juventus.
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