The Sun says he Blues owner met with AC Milan chief Ancelotti in Geneva on Monday to discuss his options.
The discussions followed a similar talk with England manager Fabio Capello in Moscow last week.
Red Rom spent around 45 minutes with the Italian after Chelsea's shootout defeat to Manchester United in the Champions League final.
Blackburn boss and former Chelsea player Mark Hughes is also in the frame to succeed Avram Grant.
But Abramovich is determined to take his time and get the right man this time.