Former Jet Airways chairman Naresh Goyal and his wife were stopped by Mumbai immigration from travelling abroad, news agency PTI reported on Saturday.
A lookout circular has been put out against the Jet Airways founders, officials say.
The Serious Fraud Investigation office and the Enforcement Directorate have reportedly started inquiring into the Jet Airways crisis.
Recently, top executives of the airline resigned.
The airline is struggling with a debt of more than $1.2 billion, and owes money to lessors, suppliers, pilots and oil companies. Lenders of the now-grounded Jet Airways have taken a controlling stake in the airline, and are currently in the process of selling a stake to recover their dues.
The airline temporarily suspended its flight operations on April 17. Read more