The Monetary Authority of Singapore issued a statement following a report by The Australian newspaper saying that it has asked about 40 banks with operations in the city-state to provide information on the matter.
"MAS is able to confirm that as part of its investigations into possible money-laundering and other offences in Singapore, it has been conducting a thorough review of various transactions as well as fund flows through our banking system," the central bank said.
It also said it was working closely with authorities in other financial centres because of the cross-border nature of the fund flows.
"Besides any enforcement actions by the relevant authorities in Singapore for possible violations of our laws, MAS will not hesitate to take regulatory actions against financial institutions should they be found to have breached our banking rules," MAS said.
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Transfers of as little as 50,000 Australian dollar (USD 38,365) are believed to be under scrutiny by the MAS, which is investigating whether the haul was split into small amounts in a bid to escape notice, The Australian said.
Najib is under pressure to explain why he accepted hundreds of millions of dollars in mysterious overseas payments to his personal bank accounts that the Wall Street Journal said were used to fund lavish spending and payouts to political figures ahead of 2013 elections.
Najib, 62, has repeatedly denied that the money was siphoned off from 1Malaysia Development Berhad (1MDB), and says he is the victim of a political conspiracy.
US authorities are reportedly looking into 1MDB-related fund flows, while Swiss, British, Hong Kong and Luxembourg authorities are also scrutinising them.