Ibrahimovic has become a free agent since he ended his two-year spell in MLS with LA Galaxy last month.
- When does the transfer window reopen?
- All major completed transfer deals
Ancelotti worked with the striker at Paris Saint-Germain during the 2012-13 season where they won the Ligue 1 title.
"He is a good friend of mine," Ancelotti told a news conference. "I have trained a lot of fantastic players. I know he finishes his period in the United States, I don't know what his idea is.
"I have to call him, maybe I call him. If he wants to come to Liverpool to enjoy he can come -- but not to play!"
Ibrahimovic has been linked with a return to Serie A with AC Milan but the club's directorZvonimir Boban recently said a deal was unlikely.
Ancelotti, one of Europe's most successful coaches who won the Premier League with Chelsea and Champions League with AC Milan and Real Madrid, left Napoli this month and replaced Marco Silva who was sacked after a 5-2 loss to Liverpool left them in the relegation zone.
Everton, now 15th after finding a measure of stability under interim boss Duncan Ferguson, submitted a planning application for their proposed new 52,000-seater Bramley-Moore Dock stadium on Monday.
"The club wants to be competitive in the Premier League, for me this is enough," Ancelotti said. "The fact the club wants to build a new stadium... That means the ambition of the club is very high. This is what attracted me.
"We want to try and play attractive football. I see how the supporters drive the team forward, this is good. The long-term objective is to be competitive in the Premier League.
"I have my idea of this team and squad... I want to try my best to help the team to be better and to help the club to be competitive and to give happiness to supporters.
"They've had a lot of time without winning so we have to be passionate with a clear focus... It'll not be overnight but we have to be patient. I'm sure we're going to improve quickly."
Ancelotti confirmed Ferguson would stay on in his coaching staff because he was familiar with the players, saying he had done the same at PSG with Claude Makelele and Real Madrid with Zinedine Zidane.
"Duncan will be on my staff and my assistant," Ancelotti said. "This is important, Duncan knows really well the characteristics of the players, the atmosphere at the training ground. It'll be really helpful for me.
"Duncan has done a great job, the players showed a great spirit [in the weekend's draw] against Arsenal."
Ancelotti will take charge of his first game as Everton boss when they welcome Burnley to Goodison Park on Boxing Day.
Information from Reuters was used in this report.
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