The commissioner may impose heavy penalty on the duo for the violations of the law, they said.
The investigations against event manager Chitresh Shrivastava, who is also under detention, and two foreign exchange dealers of Mumbai, would continue, the sources said.
The agency had conducted the exhaustive questioning of Rahat, 37, and Maroof about the money, regarding payments received during their shows in the country and channels of money transfer. It had also questioned a number of other persons in the case, which included his event managers.
Meanwhile, the agency sleuths had also swooped down the premises of "Eyeline Telefilm and Events" in Mumbai, owned by Chitresh Shrivastava, elder brother of Bollywood singer Aadesh Shrivastava, and searched the premises, they said.
Sources privy to the investigations claimed the sleuths found Rs 51 lakh in cash from the company, which was seized besides some documents which could be helpful in the probe being carried out by the DRI.
Rahat and his entire 16-member troupe, including Maroof and the event manager, were detained by the authorities. The troupe was on in its way to Lahore via Dubai.
As per norms, no one can carry beyond $ 5,000 in cash and $ 5,000 in other instruments. A person has to declare the amount if he is carrying more than this to the customs department.
According to sources, the payments by an event manager to Rahat were made in Indian currency and US dollars and these people were allegedly found converting the dollars to Indian rupees "through unauthorised channels".
Rahat is rated as a one of the top playback singers of Hindi film industry who has several hit numbers to his credit. He won the Filmfare Award for Best Male Playback Singer this year for Dil To Bachcha Hai Ji from the movie Ishqiya.