The Blues had not won a Premier League win November 10 until last night's 1-0 defeat of Bolton, taking just three points from six games during that time and slipping out of the top four - their worst run since 1998.
The relationship between Ancelotti and club owner Roman Abramovich is reported to be strained but Hiddink's agent insists his man will not be taking any leave from managing the Turkish national team even if Chelsea come knocking like they did in 2009 following the departure of Luiz Felipe Scolari.
Here's one I won earlier: Guus Hiddink with the FA Cup in 2009
Hiddink and Abramovich are friends after working together during his time as Russia boss as well as the three-month Stamford Bridge stint in 2009 that ended with victory in the FA Cup Final.
However, Cees van Nieuwenhuizen has warned the champions that Hiddink is not for hire this time.
He told The Independent: 'That is impossible. It was much easier before (in 2009) for us to come to an agreementwith the Russian Federation, as his job there was partly paid for byAbramovich. We were able to look at it in a different way.
Close friends: Guus Hiddink (left) and Chelsea owner Roman Abramovich
'Now it is quite a challenge for Turkey to achieve qualification toEuro 2012. I think the Turkish Federation would never allow him to do adouble job.
'And Guus would never consider walking out on the Turkish Federation tocome to London. He enjoyed very much his time at Chelsea. But there isno chance, no chance, of him going back.'
Hiddink, 64, is only six months into a four-year contract with the Turkish FA.
LEO SPALL: Who was Arsenal's all-action hero against Chelsea? Theo Walcott, it's a no-brainerArsenal and Chelsea eye 16-year-old 'new Dzeko' - Hannover striker Kasumovic Chelsea out of control: Woe deepens for Ancelotti's men after Arsenal defeatArsenal 3 Chelsea 1: Gunners on fire as Walcott hands Carlo nightmareChelsea '90% certain' to land Kaka as Brazilian eyes Ancelotti reunionCHELSEA FC