Carneiro was criticised by Mourinho for running onto the pitch to treat Eden Hazard on the opening day of the season with Chelsea looking for a late winner against Swansea.
She was resultantly dropped from first team duties before leaving the club altogether.
The 42-year-old is suing Chelsea for constructive dismissal and is in a separate legal battle with former Stamford Bridge chief Mourinho, who she alleges to have victimised and discriminated against her.
The case was heard at a private hearing on Monday , with Carneiro, Roman Abromich and Chelsea's lawyers all in attendance.
Chelsea were expected to push for a settlement to avoid the case going to a public tribunal, but it is believed a settlement has not been reached.
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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.
Depending on what comes out in the public tribunal, Mourinho's expected move to Manchester United in the summer could be thrown into serious doubt.
After Monday'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.
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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 was dropped as Chelsea's first-team doctor last year after then-manager Mourinho angrily berated her and physio Jon Fearn after they went on to 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".
BPI
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.
