Modi, whose jewellery creations are popular among global celebrities, may face a fresh CBI probe as the agency is looking at suitable legal action to be taken in the case.
He is already being investigated by the CBI for alleged cheating and fraud involving Rs 280 crore at a PNB branch, the officials said.
They said it had received two complaints from the PNB yesterday in which it was alleged that the bank had spotted fraudulent transactions worth over Rs 11,400 crore involving Modi and a jewellery company.
It was not immediately clear whether the jewellery company mentioned in the complaints was linked to Modi.
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Meanwhile, the bank had also intimated stock exchange BSE about the "fraudulent and unauthorized" transactions worth over USD 1771.69 million in one of its branches in Mumbai.
In its filing at the BSE, the PNB said the bank had detected some fraudulent and unauthorised transactions in a Mumbai branch.
The intimation did not say if these transactions were linked to Modi.
The officials in the agency, however, confirmed that the transactions cited by the bank in its complaint were linked to Modi and a jewellery company, whose name they have withheld.
No official comments were available from the agency on the issue or the nature of the transaction.
The designer, himself a celebrity, grew up in Belgium's Antwerp--the diamond capital of the world -- and started his own brand by the name of "Nirav Modi".