Dr Carneiro was criticised by former Chelsea manager Mourinho and dropped from first-team duties after she rushed on to the pitch to treat Eden Hazard during a draw with Swansea on the opening day of the Premier League season last August.
She is suing Chelsea for constructive dismissal and has a separate personal legal action against Mourinho, who left the club in December, for alleged victimisation and discrimination.
After yesterday’s private hearing at the London South Employment Tribunal, Dr Carneiro’s barrister Mary O’Rourke QC refused to be drawn on whether a deal had been reached, saying: “Mediation proceedings are confidential.”
Dr Carneiro refused to speak to the media as she left the employment tribunal building in Croydon accompanied by her husband, polar explorer Jason De Carteret, but shook her head briefly when asked if a resolution had been reached.
Lawyers for the three parties are believed to have failed to reach a financial deal during a private hearing that lasted around six-and-a-half hours, meaning the case is now likely to go to a full employment tribunal, expected to be held in June.
That would be held in public and could see Mourinho, Dr Carneiro and representatives from Chelsea called to appear as witnesses.
Statements and documents such as emails and text messages would also be likely to be made public.
Before Monday’s private hearing, Ms O’Rourke called for Mourinho to make a “public apology” to her client.
The former Chelsea boss was not present at the hearing.
Dr Carneiro, 42, was dropped as Chelsea’s first-team doctor last year after then-manager Mourinho angrily berated her and physio Jon Fearn after they went onto the pitch at Stamford Bridge to treat the injured Hazard during the second half, as the Blues struggled to a 2-2 draw.
Their action meant that Chelsea were temporarily down to nine men, and afterwards Mourinho called Dr Carneiro and Mr Fearn “impulsive and naive”.
Dr Carneiro did not appear on the bench again for first-team duties and later parted company with the club.
Chelsea filed their defence in the tribunal hearing in December and another private preliminary hearing was held in January.
Mourinho was cleared of using discriminatory language towards her following an investigation by the Football Association.
Afterwards, Dr Carneiro and the FA’s independent board member, Dame Heather Rabbatts, criticised the governing body for not interviewing the doctor as part of its investigation.
Dr Carneiro has also had support from Fifa’s medical chairman, Michel D’Hooghe, who contacted the doctor to offer his support and that of the world governing body. He has backed Dr Carneiro’s insistence that she was simply doing her job.