The Italian has faced increasing pressure in the job in recent months, with supporters protesting against him during an FA Cup defeat to Manchester United last month.
However, The Sun reported on Friday that the former Napoli boss will remain in charge until the end of the season, unless his team are knocked out of the Europa League and their top-four hopes crumble in the Premier League.
The leading contenders to replace him in the summer are now Nuno and Derby County boss Lampard, according to the newspaper, after top target Zinedine Zidane returned to Real Madrid.
Nuno is said to be a popular option with the Stamford Bridge hierarchy after impressively taking Wolves to seventh place and an FA Cup semi-final in his first season in the Premier League, after achieving promotion last year.
However, fan favourite Lampard is also an option as he approaches the end of his first season in senior management, with his Rams side pushing for a play-off spot in the Championship.
Derby are eighth in the second tier as it stands, one point behind Aston Villa in sixth and two points adrift of fifth-placed Middlesbrough.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.