Essien, who returned to Stamford Bridge after a loan spell at Real Madrid last season, says he is a huge fan of the way both coaches conduct themselves in front of the media.
And the Ghana midfielder is hoping to be “delighted” by the pair’s sense of humour around the Blues’ clashes with the Eagles this season.
“I can’t wait for Chelsea v Crystal Palace, both home and away – not only for the football but for the press conferences of both managers,” Essien wrote on his blog on Chelsea’s website.
“In my view the two funniest press conference managers – José Mourinho v Ian Holloway.
“Apart from taking their respective games and team performances seriously, they bring a lighter side to football.
“Whenever I listen to them, they make me laugh so much and they show that football needs and has a sense of humour.
“They are two brilliant coaches who have achieved so much for their various teams and know how to entertain on and off the pitch.
“I hope they both appear on the same stage and delight us all with their sense of humour. Comic relief should get them to do a piece to raise funds for charity if possible.”
Chelsea host Palace at Stamford Bridge on 14 December, before the return fixture at Selhurst Park on 29 March.