Chairman Naresh Goyal, who was in Mumbai last week, reportedly discussed the issue with Datta, a veteran of over 46 years in the airline industry.
Jet Airways has officially strongly denied Datta's exit. In an interview to Business Standard a few weeks ago Datta, however, was non-committal. "I have been in this sector for 46 years. Is that not long enough?" he asked.
On the specific question of whether he was leaving, Datta merely said: "I do not want to comment on speculation. I will talk about it when the time comes.''
Insiders said if Datta leaves it will primarily be for personal reasons and the fact that he has worked for so many decades in Jet rather than reported opposition to the airline's policy to hire expatriate managers.
Datta himself had denied this as a reason, saying, "All the expats are experienced and we are working together for the improvement of the airline."
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Last month, three of Jet's senior executives left the airline, which has been recruiting expatriates in key positions. Jet recently hired ex-Singapore Airlines executive Sudheer Raghavan as executive vice-president (commercial) in place of Carl Saldhana.
Abdulrahman Albusaidy, earlier with Oman Air, has also joined. The CEO of JetLite, formerly Sahara Air and now Jet's low-cost subsidiary, is Maunu von Lueders from Finnair.
Jet also replaced Murali Ramchandaran, its senior manager, airport services, with another expat of Indian origin, Jairaj Singaporia, who was formerly with Singapore Airlines.
Jet is one of the carriers with the maximum number of foreign pilots on its rolls