The Swedish international, who turns 40 in October, has been credited with turning Milan into title contenders again since his return to the Serie A club in January last year.
"For Ibrahimovic there are only small details missing, we are very close to renewal," Maldini said before Milan's Serie A game at Parma.
Ibrahimovic, who helped Milan to their last Serie A title in 2011, is the club's top scorer with 15 goals in 16 games having missed others through injury and illness. The former Manchester United, Paris Saint-Germain and Barcelona forward's current deal runs until the end of the season with discussions about an extension until June 2022.
The Swede returned to the national team last month, more than five years after calling time on his international career. Meanwhile, contract talks with Milan goalkeeper Gianluigi Donnarumma are less advanced.