She was asked to return to work last Friday, but did not show up – and now the Daily Mail report she has parted company with the club.
The FA is also reportedly looking into whether Mourinho had used abusive and/or sexist language aimed at Carneiro.
Manager Jose Mourinho branded Carneiro and physiotherapist Jon Fearn “naive” for entering the field to treat Hazard, despite them being waved on by referee Michael Oliver.
Chelsea were then temporarily reduced to nine men against Swansea as the Belgian had to leave the field promting a furious response from Mourinho.
Carneiro, 42 lost her place on the bench and was no longer allowed to attend matches or training sessions, the BBC said. This incident and Dr Carneiro’s subsequent demotion has made her position untenable.
Heather Rabbatts, an FA board member, said on Tuesday that Carneiro’s impending exit filled her with “sadness and anger”.
Chelsea may argue that her failure to turn up for work could weaken her case for constructive dismissal, even though arriving at Cobham could have amounted to accepting new terms of employment after she was publicly stripped of first-team duties.
Mourinho has been heavily criticised by many sections of the footballing world, especially since Eden Hazard could have been severely injured and had Eva not gone onto the pitch, it could have been a major problem for the winger.
A spokesperson for the group Women in Football said: ” We are bitterly disappointed about the departure of Dr Eva Carneiro from Chelsea FC”.
It is understood that Carneiro has high level support from within Chelsea and the ongoing saga could be seen as potentially damaging for Mourinho.
“The footage of the abuse she has endured in silence from the stands during her career is something we should all be ashamed of”.
The issue of team doctors has been discussed by the Federation Internationale de Football Association medical committee as a result of the incident.
Carneiro was supported by the Professional Footballers’ Association chief executive Gordon Taylor.
Mourinho should be fined or banned for a game or two as he denied a doctor from carrying out her duty to treat an injured player, at least Mourinho was trying to do that. It is the Hippocratic oath.
The evidence given to FA, which includes a person’s testimony from the audience, allegedly says the manager called Carneiro “filha de puta” (daughter of a whore) in their native Portuguese.