The deal initialed last week between the United States and Switzerland over UBS will involve the disclosure of around 5,000 holders of secret Swiss accounts, weekly newspaper NZZ am Sonntag said on Sunday.
Another Swiss weekly, Sonntag, said around 4,500 names would be handed over.
The landmark deal, ending a dispute in which the U.S. tax authorities had sued UBS to disclose 52,000 U.S. clients suspected of tax evasion, dispels a big cloud hanging over the world's second biggest wealth manager.
It also formally leaves Switzerland's cherished banking secrecy intact, although many Swiss private bankers say it has been badly damaged.
NZZ am Sonntag, citing its own researches and reports in the U.S. press, said the deal would be based on the existing U.S.-Swiss double taxation agreement of 1996, and therefore not require any changes to Swiss law.
As a result, the Swiss cabinet will be able to implement the deal directly, without going through parliament, it said.
UBS will also escape having to pay a fine, it said.
The deal will probably be signed this week, a source familiar with the situation told Reuters on Friday.
A spokesman for the Swiss justice department declined to comment, noting that the two sides had agreed not to release details of the deal until it is signed. A spokesman for UBS also declined to comment.
NZZ am Sonntag said the names of those to be disclosed would be those suspected of committing tax fraud under the terms of the double taxation agreement, which obliges Switzerland to provide help if Washington seeks it in a criminal investigation.
Accounts below a certain size would not be reported, but this limit would be kept confidential so that account-holders could never be sure whether they were vulnerable, it said.
However, account-holders threatened with disclosure would be able to challenge the move in the Swiss courts, it said.
NZZ am Sonntag said the U.S. government had backed off from the original demands of the Internal Revenue Service (IRS) because the U.S. Treasury Secretary did not want to provoke another financial crisis by pushing UBS over the edge.
Under a previous agreement, UBS settled criminal charges that it had facilitated tax fraud by paying $780 million and handing over data on about 250 U.S. clients.
U.S. prosecutors said on Friday that a California client of UBS would plead guilty to criminal charges arising from an investigation into tax evasion at UBS, the fourth prosecution arising from that deal.
Criminal charges arising from that case, and the disclosure of further names from the latest deal are keeping pressure on suspected offenders to report themselves voluntarily under an amnesty program running to September 23.
Sonntag said that the total amount of fines likely to be paid by account-holders disclosed in last week's deal would be around 4 billion Swiss francs ($3.74 billion).
But it said a British lawyer was already trying to drum up support for a class action by UBS customers who feel they have been betrayed by the bank.
It quoted Konrad Hummler, partner in Swiss private bank Wegelin, as saying that Swiss banks would suffer from any further disclosure of customer data by UBS, even if in purely formal terms that did not breach Swiss law or banking secrecy.
Everyone is talking about success -- the IRS, the Swiss government, UBS. But that can't possibly be the case, he said.
Although we still don't know any of the details, we can guess some things: the customer has been made a fool of -- he was promised something which retroactively no longer applies, he said.
($1=1.070 Swiss Franc)
(Editing by Jon Loades-Carter)