The 48-year-old took charge of Lazio in July, four months after leaving his post as Italy coach after the national team missed out on a third consecutive World Cup.
As an AC Milan player between 1999 and 2012, Gattuso won two Serie A titles and two Champions League trophies, but he has yet to reach similar heights as a coach.
The 2006 World Cup winner has also managed Fiorentina, Valencia, Napoli and Marseille.
Lazio were the only one of the 12 Serie A clubs competing in the last 64 of the tournament to be knocked out.
Seven-time Italian Cup winners, Lazio lost last season's final to Inter Milan in May.