The club sit just one point above the relegation zone after losing nine of their 16 games this season
Here Press Association Sport looks at the candidates to succeed the self-proclaimed Special One
:: Carlo Ancelotti
Will Chelsea return for another man who enjoyed great success? The Italian, who won the 2010 Premier League and FA Cup double and finished second the following season before being sacked, is available after leaving Real Madrid
He was popular at Stamford Bridge and apparently wishes to return to England.
:: Pep Guardiola
The former Barcelona boss was reportedly coveted by Roman Abramovich while on sabbatical before the former Spain midfielder opted for Bayern Munich
His contract with the Bavarians ends this summer and speculation of a switch to Manchester City is growing in strength
But Chelsea may still try to tempt him.
:: Diego Simeone
The former Argentina midfielder has enjoyed a fine period as Atletico Madrid boss, breaching the hegemony of Barca and rivals Real with an attractive style, while beating Chelsea in the UEFA Super Cup and Champions League in the process
The Blues have looked to Atletico for players, now for a manager?
:: Fabio Capello
The autocratic Italian's reputation in England is far from strong after his poor reign as national team boss
But his club pedigree with AC Milan and Real Madrid is good and he is still in touch with his former England captain John Terry
He is out of work after leaving Russia and could be an interim option.
:: Guus Hiddink
If Chelsea need a stop-gap option, they could look to someone who has done the job before
No, not Rafael Benitez, who is now Real Madrid boss, but Dutchman Hiddink
His three-month spell from February 2009, after the departure of Luiz Felipe Scolari, saw Chelsea win the FA Cup and finish third in the Premier League.
:: Antonio Conte
The Italy boss may not move ahead of Euro 2016, but reportedly has admirers among the Chelsea hierarchy
He had a glowing caeer at Juventus, first as a player, then as a manager, guiding them to three successive Serie A titles.
:: Massimiliano Allegri
The Italian led Juventus to the Serie A title and Champions League final in 2015 and could be an outside bet to replace Mourinho, but Chelsea have made bold choices in the past and it could happen again.
:: John Terry
The club captain, now 35, has been reading management books for the last few years and recently had Sir Alex Ferguson's "Leading" for company on a flight back from a match
Some have argued Terry has been in charge of Chelsea for years, maybe he could be handed the opportunity to prove it.
:: Juande Ramos
Former Tottenham boss would be a left-field appointment but has been mentioned often over recent days
Has has a long and well-travelled career and most recently took charge of Dnipro
Would in no way be a long-term appointment.
Source : PA
Source: PA