It said a letter left near the scene of the attack on Tuesday claimed it was in retaliation for German military reconnaissance missions against Islamic State in Syria.
German investigators are also examining a second letter claiming responsibility for the attack that injured player Marc Bartra, Focus online magazine said on Wednesday
German investigators are looking into the possibility that explosions targeting a bus carrying players of soccer club Borussia Dortmund may have been carried out by Islamists militants, the Sueddeutsche Zeitung newspaper reported on Wednesday.
It said a letter left near the scene of the attack on Tuesday claimed it was in retaliation for German military reconnaissance missions against Islamic State in Syria.
The newspaper also said that the letter might be a deliberate attempt by the perpetrators to mislead investigators.
The Federal Public Prosecutor said in a statement it had taken over the investigation and would hold a news conference at 2:00 pm (1200 GMT).
German investigators are also examining a second letter claiming responsibility for the attack that injured player Marc Bartra, Focus online magazine said on Wednesday.
It said a message posted on an anti-fascism online portal said the attack was in retaliation for what the letter called the soccer club's soft approach toward neo-Nazi and racist fans.
Earlier on Tuesday, Germany's best-selling Bild daily quoted anonymous sources saying that investigators were hunting for a likely getaway car used by the attacker.
The vehicle had foreign car plates, said the newspaper, which also added that police believed the explosives were a particular type of pipe-bomb.
Dortmund police said security would be tightened at Wednesday's match, with a major deployment of officers to "ensure that the game is played safely".
Separately, security was also being tightened at the Bayern-Real tie in Munich.
Bild said both teams' hotels were under heavy police guard, and the squads' buses driven to a safe location.
