West Ham's poor form is a hangover from a disappointing season last term which ended with a satisfactory 11th place finish but came after a number of flirtations with the relegation battle.
The likes of Thomas Tuchel, Rafa Benitez and Roberto Mancini have been linked as possible replacements for Bilic.
Now after his sacking from German giants Bayern, former Chelsea and Real Madrid boss Ancelotti is the latest to be linked, as reported by the likes of The Daily Mail.
There would likely be a queue of clubs from across Europe for Ancelotti's signature.
But comments from the Italian's first interview since his sacking offer encouragement to West Ham after he confirmed his desire to return to the Premier League - where he enjoyed his time in London managing Chelsea.
"I want to manage," Ancelotti told Sky Sports.
"Not this season, maybe next season (either) in the Premier League or at another club.
"The only thing I want to do is to train."
Back in 2011, the then Chelsea manager told the now defunct News of the World he would happily manage newly-relegated West Ham to stay in English football as speculation swirled that he would be replaced by the Blues.
"I would coach West Ham - why not,” he told News of the World.
"It's a challenge to manage a team outside of the top four and even in the Championship. The atmosphere at West Ham is amazing and I can say the same about football in the Championship."