The officials said the ministry would vehemently oppose Goyal's plea seeking permission to travel abroad, especially considering the public interest involved.
Thousands of the airline's employees have not been paid their salaries and the banks have also been left high and dry. Against this backdrop, the ministry would oppose Goyal's plea, the officials added.
Goyal's plea is to be heard on Friday by Justice Vibhu Bakhru.
A Look Out Circular is issued against a person directing the immigration authorities to ensure that he or she does not leave India through an airport or a seaport.
Naresh and Anita Goyal had resigned from the board of Jet Airways, which the former founded 26 years ago, in March following a debt restructuring plan. He had also resigned as the airline's chairman.
Jet Airways is currently undergoing insolvency proceedings.
Meanwhile, the ministry has also ordered a probe by the Serious Fraud Investigation Office (SFIO) into the affairs of Jet Airways.