The Russian owner appointed the Italian in 2009 and he went onto win the double before being axed two years later.
Ancelotti, now boss of Napoli, is still highly regarded among Blues staff and supporters.
And it is has been revealed that he remained in contact with Abramovich and the pair shared text messages over the team's struggles.
Sky Italian journalist Fabio Caressa admitted: "Ancelotti told me that Abramovich also texted him, always the same, especially in times when things were not going well.
"He only sent him a question mark.
"Instead he, the genius, that is, Carlo, answered him only with an exclamation mark."
It appears that the 59-year-old was in no mood to give his former club any of his wisdom.
Chelsea may have needed it at times this season with his Italian compatriot Maurizio Sarri coming under increasing pressure over team selection and performances.
One ongoing issue is the failure to get the best out of £57million summer signing Jorginho.
His position in central midfielder has meant N'Golo Kante has been shifted away from his favoured anchoring role.
But Sarri insists it is the fault of Jorginho's team-mates that has led to his struggles.
He said: “Jorginho needs movement without the ball from the other players because he is used to playing one touch and it’s very difficult to play one touch without the movement of the other players.
"So the team in the first 25-30 minutes (against Huddersfield) played very well, we have movements without the ball and for Jorginho it’s easier I think.
"We played our football because we moved the ball fast, very well.
"We didn’t play our backs to the opposing goal like in the last match but we attacked the spaces, so we played our football.”
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