Ibrahimovic opened the scoring with a stunning first-half free-kick in Thursday's (AEDT) 3-0 victory at Genoa, a result that moved Milan within a point of leaders Napoli, who squandered a 2-0 lead in a 2-2 draw against Sassuolo.
The victory was a welcome return to form for Milan, having gone from unbeaten domestically to licking its wounds following back-to-back league defeats.
Milan head coach Stefano Pioli signed a contract extension last week and Ibrahimovic wants to be the next to put pen to paper as the evergreen 40-year-old eyes silverware with the club.
"I have fun, before the match, we had already decided how long I would have played," Ibrahimovic said after the match. "These guys make me have fun and feel young.
"We had made errors that cost us the previous two games. It was all our fault, not our opponents' merit, but we won today and we remain up there.
"Now I have to renew. I am happy for [Pioli] because he deserves [his contract extension], if he renews, I renew. Pioli has done a great job.
"I am happy for the fans. For so many years, they have not enjoyed as they are enjoying now. I want to make them happy, but if we don't win a trophy we haven't done anything."
Ibrahimovic's goal was his 153rd goal in Serie A, drawing level with Stefano Nyers and Hernan Crespo in 26th place among the top scorers in the Italian competition.
His 73 league goals for Milan also took Swedish forward Ibrahimovic to 10th in Milan's standings, alongside Filippo Inzaghi.
Once Pioli had penned his own terms, the 56-year-old revealed that Ibrahimovic wasted no time in contacting him to ask for a new contract.
The Milan boss praised his team's performance against Genoa, particularly the connection between Ibrahimovic and his team-mates.
"Zlatan is the only player who sent me a message as soon as I signed my contract," Pioli said to Sky Sport Italia. "It said congratulations, Mister, now sort mine out!
"That's Zlatan for you! This is a season that can give us satisfaction, I don't know how far we can go.
"We played with intensity and determination for the whole game this evening and unfortunately we are not a team that can do the bare minimum. We've got to give it our all, or we are not superior to the opposition.
"The arrival of Zlatan improved everything, certainly, but his team-mates also did well to accept his way of motivating them.
"At the same time, Zlatan has to thank his team-ates, because he has come back to being the great player he was a few years ago. It's give and take for them both."