Carneiro is taking legal action against Chelsea for constructive dismissal and arrived at a tribunal in Croydon on Monday.
Should the 42-year-old doctor fail to agree a settlement with her former club, the case will be moved to a public hearing later this year.
Carneiro’s barrister, Mary O’Rourke QC, told ITV: “We’re not expecting a resolution today.
The two sides are so far apart financially. And we want Mr Mourinho to make a public apology.”
Carneiro was publicly criticised and labelled “naive” by Mourinho for running onto the pitch to treat Eden Hazard in Chelsea’s draw with Swansea City on the opening day of the season.
She was then stripped of her first-team duties before leaving the club in September.
In September, the Football Association confirmed that Mourinho would face no charges over his comments towards Carneiro.