The result, which the European Central Bank (ECB) and others hope will persuade investors that the European Union is finally coming clean about the extent of banks' problems, will pressure reluctant states to prop up lenders that cannot raise money.
Eurozone sources said the European Banking Authority (EBA) was set to announce within weeks that 10-15 of 91 banks being scrutinised had failed, with casualties expected in Germany, Greece, Portugal and Spain.
The checks will provide the first picture of the health of EU banks since a previous round a year ago was deemed too lax.
In that round, Irish banks were all given a clean bill of health months before their difficulties drove the country to seek an international bailout.
The new checks will measure how well the core capital that banks rely on to absorb losses such as unpaid loans holds up when exposed to an economic dip or fall in property prices.
They also gauge the impact on banks should government bonds they own, issued by states such as Greece, lose value. But the tests stop short of assessing the full impact of a country defaulting, including the likely resultant freeze in interbank lending.
In the drive for credibility, the EBA, which runs the tests and the ECB, which sets the economic scenarios, have pushed for more banks to fail than last year's seven.
"How many do we expect to fail? I would say 10 to 15," said one senior eurozone central banking source.
The EBA wants the number of banks that do not pass the tests to be around that level to show the examinations were serious, said a second source, adding that the authority did not want to push for more, for fear it could spark panic.
"In order to demonstrate that it is credible, the EBA would need to show that the number of bank failures is significant, without being substantial," said the source. "A number in the teens is about right."
A spokeswoman for the EBA said testing was still under way and declined to comment on speculation about the outcome.
Technical and political tests
The tests are technical, as well as political. While the EBA and ECB want to show up the failures, national regulators want to stop their banks appearing on the list, concerned they would look incompetent for not having spotted problems themselves.
EU authorities want to expose laggard groups around the EU, said the second source, avoiding too many problems in weak countries, such as Spain, as that could prompt international lenders to shun the country and its banks.
"They are going to find a way of preventing one centre [...] from sticking out," said the source. "If it were to be Spain, it would be very bad news. Failing German banks in a stress test would be much safer."
The EBA, due to announce the results in mid-July to coincide with a meeting of EU finance ministers, also faces pressure from governments wanting to avoid flops that may force them to come up with financial support.
One EU official said disagreement with Germany over how to apply the stress-test criteria had delayed the conclusion of the bank checks by some weeks, until July.
German regulators, who privately deny they upset the timetable by refusing to apply the criteria agreed, blame imprecise EBA templates and say the stress tests could be delayed again beyond the middle of July.
"Every national regulator will be fighting for none of their banks to be on the list," said the source. "It is a mark of incompetence. It is a reputational issue and it is an issue of money."
High-level officials from European finance ministries are now working on how to help those given a failing grade.
Andrea Enria, head of the EBA, last week called on governments to put plans in place to help banks that failed or were shown to be vulnerable.
Yesterday (28 June), a spokeswoman for the EBA said governments must not be slow to plug any capital holes exposed in the checks.
"It is important that concrete and decisive actions by the banks and authorities are taken following the results, including ensuring that credible capital plans [...] are taken to address deficiencies."
Although the EBA is insisting on the publication of each bank's sovereign debt holdings by maturity as well as size, it is ultimately the number of banks which fail that will establish the credibility of the checks.
"If it was the same as last time when seven failed, next to nothing, then no-one would believe it," said one source. "But you cannot fail 50, or the banking system would collapse."
EurActiv with Reuters