The Italian has previously worked with an enigmatic frontman at Paris Saint-Germain and may look to add him to his ranks at Goodison Park
Carlo Ancelotti has left the door open for his “good friend” Zlatan Ibrahimovic to join him at Everton, with the Swedish striker available as a free agent.
Various landing spots have been mooted for the enigmatic frontman after deciding to bring an end to a spell in MLS with the LA Galaxy.
It appeared at one stage as though a return to Italy would be made by the former Juventus, Inter and AC Milan star.
No deal has been done for the 38-year-old, though, and a second stint in England is also being speculated on for a man who has previously enjoyed success at Manchester United.
Ancelotti’s arrival at Goodison Park has seen Everton added to Ibrahimovic’s list of reported suitors.
The new Toffees boss has previously worked with a mercurial talent at Paris Saint-Germain and has suggested that he would be happy to take in a reunion on Merseyside.
When asked to address links to Ibrahimovic at his first press conference, Ancelotti said: “He is a good friend of mine. 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!”
While fuelling the speculation surrounding one striker, Ancelotti has sought to curb the rumours around another.
He claims that Moise Kean will form part of his plans despite the 19-year-old former Juventus star struggling to make his mark in England.
“I tried to sign him before he signed for Everton,” said Ancelotti, who is filling a new role after being sacked by Napoli.
“He is a fantastic player, we have to remember he is only 19. We have to wait and work with him. He has top quality.”
The challenge facing Ancelotti at Everton is to unlock the potential within their ranks and establish the kind of consistency which predecessor Marco Silva failed to deliver.
Quizzed on why a role with the Toffees appealed to him, the ex-Chelsea boss said: “The club wants to be competitive in the Premier League, for me, this is enough.
“We have to improve the right way, the fact the club wants to build a new stadium, I know that today is a very important day. That means the ambition of the club is very high.
“We want to try and play attractive football. I see how the supporters drive the team forward, this is good. I will like to try and play attractive football.
“The long-term objective is to be competitive in the Premier League – there are a lot of fantastic teams here. We want to be ambitious, this is the goal and of course to be competitive – also in Europe could be good.
“The attraction is the tradition and history of the club. It is true that I manage a top team, when I was at PSG the project was really good there and that attracted me so the ambition of the club.
“I think that is the same here. It is not true that I only manage top teams – sometimes in Italy I mange Championship teams. I like teams that have ambition and have a clear idea of how to reach success.
“I went to the training ground yesterday – it is a fantastic training ground and the fact the club want to build a new stadium shows ambition. This is what attracted me.”
Ancelotti is taking over at Goodison Park on the back of an interim spell from Duncan Ferguson as first-team coach.
The Scot earned plenty of plaudits during his short time at the helm and will be kept on within a new backroom team.
“Duncan will be on my staff and my assistant,” said Ancelotti.
“This is important – Duncan knows really well the characteristics of the player, the atmosphere at the training ground. It will be really helpful for me.”
Ancelotti first game as Everton manager will be a home date with Burnley on Boxing Day.