Coach Stefano Pioli said on Monday that Zlatan and the club are still negotiating.
But now the Swede must have decided to say yes, and the agreement with the club is expected to be signed within the next few days, according to La Gazetta dello Sport.
The information is also confirmed by journalist Gianluca Di Marzo.
According to the new agreement, Zlatan will remain in the club until June 2023.