Spanish newspaper El Pais says some of those institutions unable to pass the resilience measures have been involved in recent mergers.
Separately, Manfred Weber, the head of the Association of German Banks, says he is confident German banks “all in all” would perform well at the tests.
Results of the tests on 91 European lenders, which use scenarios including declines in the value of sovereign debt they hold, are due at 5pm.
The Financial Services Authority has already said it expects the UK banks to pass the tests.
The euro slipped 0.2% against the dollar to a session low around $1.2860 after the Spanish news, just off its levels in late U.S. trade.
The tests had been expected to show some of the unlisted savings banks would need a capital injection under certain scenarios, El Pais newspaper reports, citing financial sources.
It says a small group of savings banks would need more capital if economic conditions were to worsen sharply and there were sovereign debt crises in several countries.
Amongst these, some have already received funds from the Spanish State’s Fund for Orderly Bank Restructuring (FROB), it says, though it did not name the banks.
Goldman Sachs says its survey of investors showed they expected 10 out of the 91 assessed banks to fail, giving a pass rate of 89%.
