The incredible claim was made by respected BBC 5 Live presenter Garry Richardson during his long-established Sportsweek programme on Sunday morning.
Chelsea sources claim that the pressure on Mourinho to turn results around following their sixth defeat of the season in the Barclays Premier League — 3-1 at home by Liverpool on Saturday — has left him close to breaking point.
Richardson’s remarkable allegations have led to a whispering campaign about the identity of the mystery player, but the reality is that Mourinho’s stormy relationship with his players will ultimately cost him his job.
Richardson said: ‘Let me tell you what I know on the Chelsea story. My information comes from a Chelsea first-team player.
‘The information was actually passed to me by a football contact. I was told that Jose Mourinho’s relationship with many of his players is at rock bottom.
‘I was told they’re fed up with the way he’s been dealing with some of them. They’re fed up with his outbursts. I was told that his relationship, particularly with Eden Hazard, was under immense strain.
‘Here’s a staggering quote. One player said recently, “I’d rather lose than win for him”.
‘Now that last quote may well have been said in the heat of the moment, but it perhaps gives an insight into the mood of some of the players.’
Mourinho speaks to his coaches on the pitch after the game - Sportsmail showed footage to a lip-reader
Mourinho was more than guarded in his post-match interview, refusing to speak to BT about the game
Mourinho gave a series of bizarre post-match interviews to various television and radio stations following the defeat by Liverpool when he refused to comment on specific aspects of the game.
He then spent 15 excruciating minutes in the centre circle with various members of his backroom team as they attempted to put the club’s latest setback into some context.
Hazard’s relationship with his manager is back under the spotlight following Mourinho’s decision to haul off the PFA Player of the Year and replace him with Brazilian youngster Kenedy in the 59th minute at Stamford Bridge.
The Belgium forward tolerated Mourinho’s consistent references to him as ‘the kid’ in his first two seasons at the club, but they have a clear difference of opinion over their approach to the game.
Hazard, among others in the Chelsea squad, is tired of the football politics and criticism, both public and private, that the players have been subjected to by their demanding manager.
The 24-year-old is already determined to force a move to Real Madrid next summer if Mourinho remains in charge at the London club beyond the end of the season.
Hazard has a long-standing ambition to play for the Spanish giants he supported as a boy. He idolises the great Zinedine Zidane, who is currently coaching their nursery team.
Hazard is already determined to force a move to Real Madrid next summer if Mourinho remains in charge
Chelsea’s fractured dressing room is also missing the stabilising, soothing influence of Didier Drogba following his decision to move to MLS team Montreal Impact at the end of last season.
Despite Drogba’s limited role in the first team during the title- winning campaign last season, his seniority and presence helped to unite the team.
On Friday, Mourinho scoffed at the idea of Drogba returning to Chelsea on loan after his involvement in the MLS play-offs, but they are certainly missing the link he provides between the players and manager.
Mourinho will also be frustrated by the failure of his players to respond on Saturday against Jurgen Klopp’s side after the Chelsea manager and his coaching staff became convinced that they were back onside.
The Portuguese coach admits he has tried almost everything to motivate the players and he was sure that the performance at Stoke City in the Capital One Cup on Tuesday — even though Chelsea lost on penalties — was a breakthrough.
That appeared to be the case when Ramires converted Cesar Azpilicueta’s left-wing cross in the fourth minute against Liverpool, but beyond that the team were outplayed.
Chelsea are missing the link club legend Didier Drogba provides between the players and manager
The panic and sheer terror in the champions’ back four, comprising internationals who have represented England, France and Spain, was one of the most alarming features of the game.
Morale and confidence within the dressing room is at an all-time low and there are rumours that a number of the players are being sounded out by the hierarchy for their views on Mourinho’s disintegration.
Chelsea continued to back Mourinho over the weekend, but it has become clear that he is now managing the club on a game-by-game basis as they wait for owner Roman Abramovich to make his next move.
The Russian authorised the statement backing Mourinho following the shocking 3-1 defeat by Southampton on October 3, but it also included the caveat that results simply had to improve in the short term.
Since then they have won just once in five games and have lost three in eight days — West Ham, Stoke and Liverpool — under a man who believes he is one of the game’s super coaches.
Christian Benteke (second from left) fires Jurgen Klopp's side into a 3-1 lead at Stamford Bridge
He signed a new four-year contract, worth in excess of £10million, at the start of the season, but there are penalty clauses if Chelsea fire him again.
Abramovich was forced to pay Mourinho and his coaching staff a total of £18m when he was sacked in September 2007, a figure that was noted in the club’s published accounts the following year.
Even if he is eventually fired by Chelsea, he will have an open invitation to coach Monaco because of his agent Jorge Mendes’s close ties with their Russian owner Dmitry Rybolovlev.
Chelsea’s bedraggled players reported to Cobham on Sunday morning for a scheduled training session as Mourinho started preparations for Wednesday’s Champions League clash with Dynamo Kiev at Stamford Bridge.
Results in the Champions League have not been good — Chelsea were beaten 2-1 by Porto in their second group game — and they are third, a point behind Kiev in Group G, going into this week’s clash.
The Portuguese, who could coach Monaco, is now preparing for the midweek clash with Dynamo Kiev
