In an announcement to the stock exchange, Jet Airways did not say whether the agreement was a formal order or a non-binding memorandum of understanding. Boeing did not respond immediately to a request for comment.
The jets would be worth $8.8 billion at list prices, although airlines typically receive a significant discount from manufacturers.
Indian airlines are scrambling to add more jets to meet demand for more domestic and international flights, making it one of the most targeted sales markets for Boeing and European rival Airbus SE (AIR.PA).
Domestic Indian passenger traffic increased by 17.9 percent in January from a year earlier, marking the 41st consecutive month of double-digit growth, according to the International Air Transport Association.
Jet Airways CEO Vinay Dube last month told reporters the airline was hoping to close the deal to buy 75 narrowbody jets by the end of March.
The airline last year finalised a deal to buy a separate 75 Boeing 737 MAX aircraft.
Reporting by Jamie Freed in SINGAPORE