Deutsche Bank AG’s top executives have agreed to hold discussions with rival Commerzbank AG about a potential merger, as Germany’s two biggest banks explore strategic options after suffering prolonged performance and share-price declines, people close to the banks said.

The informal talks reflect a deepening willingness by Deutsche Bank’s management board to engage in a possible tie-up, though executives this week continued to see a potential merger as one option, some of the people said.

Heightened...