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.
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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.