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.
Football fans and some pundits have poured scorn on such reports, suggesting Ancelotti is out of West Ham's league.
But comments from Ancelotti as far back as 2011 when the Hammers were in the Championship suggest anything but.
Then Chelsea manager, the Italian 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.
"I have respect for every team and the job of my colleagues. It is the same and it doesn't matter if you can manage a top team or a smaller team.
"It's your job, and for me it's important to work. I was happy to train in the second division when I was learning.
"If a club said to me, 'You can manage this club without money', I'd have to decide whether to accept or not.
"Money is not a motivation. The money has never been a motivation for me.
"I don't think it's a motivation for the players either. It's not a strong motivation to play for the money at this level.
"The motivation is to play, to win, to be the best. To stay at the top as a player, as a manager, this is a good motivation. To give a good image of yourself, this is a good motivation.
"The Championship is also fantastic, the stadiums are fantastic. I have seen a lot of games on TV and the atmosphere is fantastic.
"If you watch a game in Italy in the second division, then in the stadium there will be say 2,000 people. It is totally different in England."
Ancelotti's words should give West Ham's owners food for thought.
And if Ancelotti was interested back then with the Hammers in the second tier, imagine his interest level now with the club packing out their new 60,000 seater London Stadium home week in week out.
While some supporters still back Bilic perhaps the opportunity to snare a manager of Ancelotti's class is too good to miss.