By Gabriele Steinhauser 

RIGA, Latvia--Some eurozone finance ministers on Saturday acknowledged for the first time that they are considering plans on what to do if no deal on Greece's future financing can be reached by the end of June.

The statements by the finance ministers of Slovenia and Germany break a long-held taboo during eurozone crisis talks, where policy makers have been insisting that they are entirely focused on keeping Greece in the currency union with the help of more bailout loans. Yet, with the country's existing EUR240 billion ($261 billion) bailout deal expiring at the end of June, and technical discussions on future support all but stuck despite big debt repayments looming in July and August, some politicians are starting to look at alternative scenarios.

Slovenia's finance minister confirmed that he raised the issue of a "Plan B" during Friday's meeting with his eurozone counterparts, also known as the Eurogroup.

"What my discussion was about is what we will do if...the new program will not be achieved in time for Greece to be able to finance itself and improve liquidity," Dusan Mramor said Saturday morning.

He denied, however, that the result of no new bailout deal would be an automatic exit of Greece from the eurozone. "A 'Plan B' can be anything, " Mr. Mramor said. Mr. Mramor's suggestion was supported at Friday's talks by the finance chiefs of Slovakia and Lithuania, according to a senior eurozone official.

Germany's finance minister, Wolfgang Schäuble, was more oblique in his response to the question of whether his country had a 'Plan B'.

"Of course there's sufficient fantasy to imagine what kinds of things could happen" if no deal on Greece's bailout can be reached, Mr. Schäuble said Saturday. "But if a responsible member of the Eurogroup, or any responsible politician, were to answer this question with 'yes,' we know what would happen. If he answered it with 'no,' which I have done here by not even accepting the question, then we know that you won't believe me."

Mr. Schäuble also likened the preparations for a potential Greek default or euro exit to the reunification of Germany--a process that commenced with the fall of the Berlin Wall in 1989.

"If I had said in advance that we had a plan for reunification, everyone would have said the Germans have gone completely mad," Mr. Schäuble said.

The former German Democratic Republic adopted the German Mark, Germany's currency before the introduction of the euro, in 1990.

Write to Gabriele Steinhauser at gabriele.steinhauser@wsj.com