A German furniture chain that inadvertently sold mugs carrying a faded image of Adolf Hitler will have to explain themselves to police, prosecutors say.

Despite the controversy, Germany’s official history museum is eager to acquire one of the coffee mugs – sold by the Zurbrueggen furniture chain in the town of Unna – to use in future exhibitions.

Prosecutor Barbara Vogelsang confirmed that an inquiry had been launched into the sale of the mugs, which are decorated with roses, handwriting in English and a Nazi-era postage stamp featuring a swastika.

Neither Zurbrueggen’s buyers nor its retail staff noticed the image before the Chinese-made mugs hit the shelves for a bargain price of 1.99 euros ($A2.96).

The chain is offering shoppers a voucher for 10 times the amount to return the mugs to its store.

The chain’s proprietor Christian Zurbrueggen said only eight of the 175 mugs sold had been returned.