Carneiro's lawyers served the papers this week after failing to agree a settlement with Chelsea, the reports said.
The three-month period in which a claim must be notified ends on Nov. 8.
Constructive dismissal involves an employer committing a serious breach of contract -- such as creating a hostile work environment -- entitling an employee to resign in response.
Carneiro left the club after a public falling out with manager Jose Mourinho, who had accused her and Jon Fearn, the Chelsea physiotherapist, of being "impulsive and naive" and failing to "understand the game" when they entered the field to treat Eden Hazard late in a match against Swansea.
Chelsea were already down to 10 men following the sending-off of goalkeeper Thibaut Courtois and Mourinho lost his temper when the pair went to treat Hazard, meaning the team were temporarily reduced to nine men.
Both Carneiro and Fearn subsequently had their first-team responsibilities curtailed, and although the physiotherapist is still at the club, Carneiro resigned last month.
The manager was widely criticised for the incident but subsequently cleared of using discriminatory language by the Football Association, while the governing body's handling of the case also drew censure from the Women in Football group, FA independent director Heather Rabbatts and Carneiro herself.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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