Borussia Dortmund attack: Iraqi suspect 'linked to IS'
But they have requested an arrest warrant to keep the 26-year-old Iraqi national in custody.
The man, identified only as Abdul Beset A, is suspected of membership in an affiliate of so-called Islamic State.
Three devices exploded on Tuesday as Borussia Dortmund footballers were travelling to a match against Monaco.
Spain international Marc Bartra underwent an operation after breaking a bone in his wrist. No other players were hurt.
The suspect is accused of leading an IS command unit in Iraq in 2014, and of planning abductions and murder.
The German prosecutors say he travelled to Turkey, and then to Germany in early 2016, while maintaining contact with IS jihadists.
He is due to appear in court later on Thursday, and is expected to be formally arrested in connection with the bus attack.
A 28-year-old German man is also under suspicion, but has not been arrested.
Source: bbc.com