Bloomberg, citing unnamed sources, said that discussions included German Finance Minister Olaf Scholz and Deutsche Bank Chief Executive Christian Sewing.

Spokesmen for the two banks declined to comment. A spokeswoman for Germany's finance ministry said there was nothing she could say about the report.

The discussions include possible ways to change laws to make a merger cheaper, Bloomberg reported. Talks are in an exploratory phase, the report said.

Shares of Deutsche Bank spiked 6.5 percent, while Commerzbank jumped 7.1 percent.

Speculation about a possible tie-up between the two banks has been rife this year. Last week Focus magazine reported that the German government was ready to orchestrate a merger between them.

Senior officials at both lenders have played down chances of a merger over the next 12 to 18 months as they restructure their companies to make them profitable.

(Reporting by Tom Sims; Editing by Michelle Martin and Maria Sheahan)