The Hamburg Prosecutor's Office said it is at an early stage of investigation, and is at least two weeks away from deciding if criminal charges will be pursued.
German authorities have demanded that Google hand over a hard drive from one of the mobile units for investigation by 26 May, but the firm has yet to agree, according to US reports.
The US Federal Trade Commission is also expected investigate whether the data collection breached rules on access to computers and private communications.
Earlier this month, Google admitted that it had collected data sent over Wi-Fi networks using its Street View cars, but said this was unintentional.
Google said the data had been collected because of experimental code that had been included by mistake in the software used by its mobile units.
The Irish Data Protection Authority last week asked Google to delete the Wi-Fi data collected in Ireland.
The UK's Information Commissioner's Office has said it will not take any action against Google because the firm had given assurances that the data will be deleted as soon as possible.
Google claims to be working with several data protection agencies to decide on how best to dispose of the Wi-Fi data.
This story was first published by Computer Weekly