The Italian was relieved of his duties at the end of the 2017/18 campaign, and was awarded £9 million in April following a breach of contract claim.
However, the Times reports that Conte – now in charge at Inter Milan – was the claimant in a preliminary hearing held at the Central London Employment Tribunal last Friday.
The former Italy and Juventus coach brought a statutory claim against Chelsea and a verdict is expected next month.
Details of it are yet to emerge, but the report suggests it will involve accusations of unfair dismissal or discrimination.
A legal source suggested to the newspaper that the 50-year-old could be looking to embarrass the Premier League club as details of the Employment Tribunal will be made public, unlike the Premier League one.
They add that the Italian is unlikely to be making the move solely for financial gain, because claims of unfair dismissal at employment tribunals are capped at £60,000.
Conte was represented by Phil Bonner of Centrefield LLP at the hearing last week, and Chelsea have the right to appeal against the verdict of the tribunal by taking the case to the High Court.
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