The speculation stems from the fact that Milan chief executive Adriano Galliani has said the club must finish third this season for Ancelotti to definitely remain. His Milan contract also runs out in 2010, meaning his future is unclear.
Below are the possible scenarios:
STAYS AT AC MILAN
Ancelotti, Serie A's longest-serving manager having been appointed in 2001, has won two European Cups with his beloved Rossoneri but their failure to challenge in the league since claiming the title in 2004 is starting to weigh on him.
The coach is adamant he wants to stay at the San Siro but he has avoided being too demanding.
"Personally I have never asked for any kind of extension, I have a contract until June 2010 which I intend to respect," he told reporters.
With third-placed Milan four points clear of Genoa with eight matches left, it looks unlikely that the Rossoneri will miss their target of automatic Champions League qualification.
Having said third place was the aim, it would be difficult for Galliani to change his mind and sack Ancelotti anyway.
Ancelotti does not want to appear a failure and, with at least two new players scheduled to be signed in the close season, he hopes to be able to mould a team that can again challenge at the top of the table and in Europe.
A contract extension would then look more likely.
STAYS UNTIL 2010, THEN LEAVES
By sticking to his contract he can hold the moral high ground and use the year to survey his options.
Ancelotti has made no secret of his interest in coaching the Italian national team.
Assuming they qualify, Marcello Lippi will lead the Azzurri to the 2010 World Cup but the job could then become available if things go badly for Lippi or he decides to quit as he did when Italy won in 2006 (only to return to the job last year).
Ancelotti would be the standout candidate to replace him.
If the Italy job was not free, recent history shows that Chelsea and Real Madrid, both seen as potential suitors in the media, get through managers quickly and an opening may arise.
LEAVES IN MAY, JOINS ANOTHER CLUB
By moving to another club immediately he is likely to gain a long-term contract and an initial feeling of job security.
Interim Chelsea coach Guus Hiddink has consistently said he will leave in May and return to coaching Russia full-time.
Ancelotti has said that Chelsea have courted him in the past and the media believe the English club are still interested.
Given ageing Milan missed the Champions League this term and were eliminated in the UEFA Cup last 16, he cannot guarantee an improvement in fortunes by 2010 and by then the Chelsea job, and possibly the Real Madrid position, could be taken.
