Ancelotti, who guided the capital club to the Ligue 1 title for the first time since 1994, has publicly revealed his desire to leave Parc des Princes this summer amid active interest from Real Madrid.
Ibrahimovic, who was signed by the former Chelsea boss in 2012, praised Ancelotti for his management skills and insisted that only a top-notch replacement would suffice should he depart before the start of the 2013-14 campaign.
“I have never had a coach like him," Ibrahimovic told Telefoot. "His method of coaching is the best. He puts responsibility on the players and I like this.
"But I don’t know anything about his future. [If he leaves] we need a top coach who can lead a continental-competing team. And that is not easy. Only the very best coaches can do it.
"I do not want Ancelotti to go. For me, he has done a fantastic job. I have had numerous coaches but not like him. He has a special relationship with players that make him the ideal guy for this job. And he is elegant."
Ibrahimovic, 31, has stormed Ligue 1 with his goals since joining AC Milan last summer, netting 29 times in 33 appearances ahead of the club's final game of the season at Lorient on Sunday, but the Swede insisted it has not all been smooth sailing.
"It was not easy for me at the beginning," Ibrahimovic said. "[Club sporting director] Leonardo warned me that PSG are not Milan. This year was not easy.
"[However] I have this confidence in me, it makes me think I can succeed wherever I go. I hope to score even more next season - that was always my goal."