The Swedish striker played under Ancelotti at PSG, and was weighing up a move to Napoli before the coach was sacked by the Serie A club earlier this month.
Now the Telegraph reports that Ibrahimovic, who is available on a free transfer in January, would be interested in teaming up with the Italian boss at Goodison Park.
Ancelotti is expected to be announced as the new Everton manager this week after completing contract talks, but Duncan Ferguson could take the reins on an interim basis for the final time at home to Arsenal on Saturday.
Negotiations with Napoli aren’t expected to provide a major obstacle, and Ancelotti could therefore be in charge by Monday.
Everton are on the hunt for a new striker and Ibrahimovic is looking for a new club after leaving LA Galaxy.
The 38-year-old has been linked with Tottenham Hotspur, AC Milan and Manchester United, but all those options now appear unlikely.
Ibrahimovic is expected to explore the possibility of joining Everton once Ancelotti is in place.
Such a move would mark a return to the Premier League for the striker, who had a spell at Manchester United from July 2016 to March 2018.
He scored 17 goals in 28 league games during his debut campaign with the Red Devils, before going on to find the net 52 times in 56 MLS appearances.
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