Carneiro is claiming constructive dismissal against Chelsea and has a separate, but connected, personal legal action against Mourinho, who left the club in December, for alleged victimisation and discrimination.
The case, which is anticipated to be heard over seven to 10 days until June 24, is due to open at Croydon Employment Tribunal in south London, but could be settled at any time.
All three parties must agree to a settlement for the tribunal, which would be accessible to the public and the media, to be averted.
Private hearings in January and February took place without a resolution and it appears the case will proceed to the tribunal.
Witness statements and documents – including texts and emails – would likely be made public, while Carneiro, Mourinho and representatives from Chelsea could be called to appear as witnesses.
It could overshadow the start of Mourinho’s employment at Old Trafford after he was named Louis van Gaal’s successor on May 27.
Chelsea have declined to comment on the case, but supported Mourinho even after his employment as manager was terminated.
Whether or not Chelsea will continue to support Mourinho now he is employed by a rival club is unclear.
Carneiro and physio Jon Fearn were criticised by Mourinho and dropped from first-team duties following the draw with Swansea on the opening day of the 2015-16 Premier League season, on August 8 2015.
Afterwards Mourinho called Carneiro and Fearn “impulsive and naive”.
The 42-year-old doctor did not appear on the bench again for first-team duties and later parted company with the club, while Fearn continues to be employed by Chelsea and returned to the first-team bench in March.
Mourinho was cleared of using discriminatory language towards Carneiro following an investigation by the Football Association.
Afterwards, Carneiro and the Football Association’s independent board member, Dame Heather Rabbatts, criticised the governing body for not interviewing the doctor as part of its investigation.
Carneiro has also had backing 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 Carneiro’s insistence that she was simply doing her job.