But Singapore banks face a more urgent challenge.
Indonesia, Singapore's main source of wealth assets, is considering offering a tax amnesty to individuals willing to repatriate funds from abroad - targeting $225 billion Jakarta says is parked in Singapore alone.
"Indonesia accounts for 30-50 percent of business for private banks in Singapore," a Singapore-based banker at a top global wealth manager told Reuters. "Clients are worried and asking about this, (while) accounting and legal firms are pitching to help clients structure their transactions," said another banker.
Both declined to be named due to client confidentiality rules.
The second banker said one client was considering whether to pass his wealth directly to one of his children, who is in the process of taking Singapore nationality.
Singapore, Asia's second-largest offshore center by assets behind Hong Kong, has thrived as a banking center due to its political and economic stability, low taxes and rule of law. It manages $470 billion of private client assets, Deloitte data show.
Read MoreSingapore at 50: From early-adopter to global leader
Singapore's central bank has said it has a rigorous regime to combat money laundering and is ready to take tough action if there are breaches. Sources said Monetary Authority of Singapore (MAS) officials have been asking private banks if they have heard any client concerns about the exchange of information mechanism. The MAS didn't comment.
The finance ministry noted that Singapore would need to sign bilateral agreements before any automatic data sharing, and those deals would depend on partner countries having a "robust" legal framework to maintain information confidentiality and "confine its use to tax purposes", a ministry spokeswoman said.
Seeking to recoup funds it first bled in the aftermath of former president Suharto's government, Jakarta is looking to introduce a tax amnesty, but has given no timetable for this.
"The idea is to first prepare the legal framework," Suahasil Nazara, who heads the fiscal policy office, told Reuters.
The planned amnesty, private bankers say, is modeled on a successful but controversial Italian tax scheme that helped Rome recoup billions of euros unlawfully parked in Switzerland against the payment of a modest penalty.
This system, which was criticized for allowing tax evaders to come clean without too much pain, is a faster way to recover funds than wading through a myriad of tax and bank data.
India, too, is trying to turn up the heat on an estimated $340 billion of undeclared wealth by its residents.
The Securities and Exchange Board of India (SEBI), the market watchdog, has asked international private banks to register their offshore units with it if they are soliciting business in India, a Reuters report revealed earlier this month.
If banks agree to register, they could be targeted by requests from SEBI to disclose client information.
"These changes will certainly make things more complicated for wealth managers. (They) will have to factor in every high net worth client's residence and domicile," said Mark Wightman, a partner for wealth & asset management at EY Advisory.
For local banks in Indonesia and elsewhere, the pressure on Singapore is opening up opportunities at home.
Read MoreFinancially-savvy Millennials: Singapore has plenty
"The hope is that with the tax amnesty, more funds will be returned to Indonesia," said Jahja Setiaatmadja, president director of Bank Central Asia, Indonesia's biggest bank by market value.
For Singapore-based banks, the move towards data sharing means radically changing a model that had been mainly based on their ability to offer strict client privacy in a low-tax environment.
Swiss wealth managers including UBS and Credit Suisse were fined by U.S. regulators for allowing clients to deposit untaxed money, and still face lawsuits elsewhere.
"Everybody's in limbo right now," said a senior banker in Singapore. "Clients are scared about opening new accounts and asking whether certain structures work."
Experts believe Singapore could continue to be an attractive center thanks to its strong legal system, security and a deep talent pool for wealth services.
"The days of undisclosed assets being held offshore will, in time, become a thing of the past," said Wightman.