The Sun says a dismal run of just one win in six matches has left the unpopular Benitez teetering on the brink.
Another setback against third-bottom Wigan could spell the end — less than three months after the Spaniard took over as manager.
Chelsea are unlikely to finish in a top-four Champions League spot on current form, having taken just five points from a possible 12.
And that would be catastrophic in their attempts to attract a top new boss and key signings in the summer.
Senior sources at the club expect ruthless Russian owner Roman Abramovich to act quickly if the depressing slump continues.
One key figure said: “Roman is loyal to Benitez and desperately wants him to stay in charge until the end of the season.
“But that loyalty will be tested to the limit if Rafa fails again.
“The be-all and end-all at this club has always been that we at least finish in the top four — and current results mean that could now be in serious doubt.
“And, let’s be honest, he has sacked managers for far less.”