Switzerland faced a renewed assault on its private banking system as Germany considered paying for secret Swiss account data detailing alleged tax evasion by about 1,500 German taxpayers.

German authorities familiar with the investigation said Sunday that a confidential informant offered to sell them the data for €2.5 million ($3.5 million). The authorities, who say the information was stolen from a Swiss bank, say officials examined samples of the data that proved to be authentic.

Swiss...