"I am really happy and honoured to manage a team with a unique city and incredible fans", said Ancelotti, as quoted by BBC Sport.
According to Sky Sports Italia, Zenit have invited the 59-year-old former banker to Russian Federation to see Saint Petersburg and their training facilities. "Well done, Maurizio - Aurelio De Laurentiis".
"He created a model of play admired everywhere and by anyone".More news: Witness greatness, as LeBron earns record 12th All-NBA First Team nod
The 49-year-old is now preparing for Fulham's Championship play-off final against Aston Villa but quit Watford after winning promotion to the Premier League in 2015.
That would sp Maurizio Sarri in Naples, clearing the way for Chelsea to appoint the 59-year-old.
Ancelotti had been linked with the Italy coaching job before Mancini's appointment.More news: NOAA predicts near- or above-normal 2018 hurricane season
Zenit are prepared to pay Sarri's €8-million (US$9.4 million) release clause, in addition to a salary worth €6 million per season plus bonuses.
Antonio Conte moved closer to the exit door at Stamford Bridge after a managerial merry-go-round started in Italy.
The Senegalese global was arguably the finest centre-back in Italy and Europe's elite are already circling.More news: Serena Williams, Venus Williams to team up in doubles at French Open
Insigne flourished under Sarri's leadership, scoring eight Serie A goals and tallying 11 assists in 2017-18.