Disagreements between Mistry and his predecessor Ratan Tata, the family patriarch and now stand-in chairman of the 148-year-old conglomerate, have turned a boardroom battle into a damaging public spat fuelled by leaked letters and tit-for-tat accusations.
Mistry alleges corporate governance failures and mismanagement at Tata, which has dismissed the allegations as "malicious".
CNBC-TV18 news channel reported on Saturday that Darius Khambatta, a senior lawyer close to both Tata and Mistry, had initiated mediation talks between the two parties. Khambatta told Reuters he was "not mediating between them," but declined to comment on whether he had met Tata and Mistry.
India's financial crime-fighting agency will look into Mistry's allegations about mismanagement at Tata's aviation ventures, another person familiar with the matter told Reuters.
In a leaked letter to the Tata board, Mistry has said he was opposed to Tata's aviation partnerships with Malaysia's AirAsia Bhd and Singapore Airlines.
In the case of Air Asia, a forensic investigation had found "fraudulent transactions" of 220 million rupees ($3.29 million) involving "non-existent parties", he alleged.
That prepared the ground for a "probe into the allegation of mismanagement of funds," said an official at the national Enforcement Directorate, on condition of anonymity.
The agency was not immediately available to comment. Tata did not respond to Reuters questions on this matter. An AirAsia India spokeswoman said she had no immediate comment.
India's capital markets regulator is already looking into Mistry's allegations related to violations of corporate governance rules at Tata.