Milan technical director Paolo Maldini has revealed Zlatan Ibrahimovic is "very close" to signing a contract extension, while Gianluigi Donnarumma has also been urged to stay at the club by head coach Stefano Pioli.
Ibrahimovic has helped to rejuvenate Milan since returning to San Siro in January 2020 on an initial six-month deal that was extended by a year ahead of the 2020-21 campaign.
The 39-year-old is due to become a free agent when his latest deal expires at the end of June.
Reports in Italy suggest the evergreen striker is happy to remain with Milan for another year, however, and Maldini has provided a positive update on the contract talks.
"There are only small details missing and therefore we are very close to the renewal," he told Sky Sport Italia.
Ibrahimovic has 25 goals in 35 Serie A appearances since the start of 2020 - only Cristiano Ronaldo (46), Ciro Immobile (33), Romelu Lukaku (32) and Luis Muriel (26) have found the net more often across this period.
Meanwhile, his scoring rate of 108.2 minutes per goal is bettered only by Muriel (58.2) and Ronaldo (84.5) among players to have scored at least five times.
The former Manchester United striker registered his seventh league assist since rejoining in Saturday's 3-1 win over Parma, although he was later sent off for dissent - the sixth red card he has received in his Serie A career.
It somewhat marred what should have been a special occasion for Ibrahimovic, who brought up his 300th career victory in Europe's 'top five' leagues - 170 of those in Serie A - thanks to his team-mates seeing the job through at Estadio Ennio Tardini.
Gianluigi Donnarumma made four saves against Parma, including an impressive quickfire double stop early in the second half to deny Andrea Conti and Graziano Pelle, highlighting his importance to the side.
The Italy international is another who could leave San Siro as a free agent in a few months, but Pioli is hopeful the club's undisputed first-choice goalkeeper will commit to fresh terms.
"I would advise Gigio to stay at Milan because it is a top club and we are building something here," he told Sky Sport Italia.
"I call my players fighters who haven't won yet, but are training to win trophies."
Hakan Calhanoglu completes the trio of Milan players with uncertain futures as he reaches the end of his contract, with the attacking midfielder reportedly holding out for a longer deal than the club are prepared to offer.
Asked for an update on the contract situations, Maldini added: "These are choices everyone has to make. I am not here to judge, I am here to do what is best for the club.
"I also know that you need two parties to be happy in order to strike a deal."
Milan, who strengthened their grip on second place with a club-record 13th away Serie A win of the season, also have the option of turning Fikayo Tomori's loan move from Chelsea into a permanent deal.
Tomori has impressed since joining in January and leads Milan defenders in blocks per 90 minutes (1.1) in Serie A this term, while the centre-back completed 93 per cent of his passes against Parma.
"He has made a wonderful impact and settled in so quickly," Pioli said. "He has other characteristics of pace and of playing out from the back that can certainly improve us as a team.
"He is a player who is certainly giving us a lot and the intention is to keep him."