Sky in Germany has been told that German police are investigating Bellingham's comments on Zwayer.
During the 3-2 loss to Zwayer, Bellingham hit out at the performance of Zwayer, as he was left frustrated after the referee turned down appeals for a penalty.
In front of a restricted attendance at Signal Iduna Park, Robert Lewandowski scored the winner against his old club.
Bellingham told ViaPlay that he didn't expect a referee to fix the biggest game in Germany.
It wasn't a penalty for me. ummels is fighting to get the ball and it hits him.
You can look at the decisions in the game.
Marco Rose was sent to the stands after he criticized the penalty award that came after a VAR review in the 77th minute.
The German FA banned Zwayer for six months in 2005 after a match-fixing scandal.
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Jude Bellingham was accused of showing "youthful inexperience" after he criticized the referee after the defeat by the Germans.
Zwayer told Sky Germany that the situation was a standard corner kick.
It's about a touch by Hummels. I was wondering if the arm was stretched away from the body. It wasn't clear if his arm was moved towards the ball.
The arm position was checked by VAR officials in Cologne.
Hummels had his arm away from the body in an unnatural position according to the video assistant.
I came to the decision that it was a penalty after he hit the ball with his elbow.
The case will be forwarded to the public prosecutor's office in the city where the incident took place, who will decide later this week if there will be criminal charges against Bellingham.
Marco Reus went down in the box in the second half but there was no VAR referral.
Even at high speed, contact can happen in the upper body area.
I decided against the penalty because of my line of sight.
Sky Sports will show the Bundesliga live for the next four seasons.
Sky Sports won exclusive rights to broadcast the next four seasons of the Bundesliga in the UK and Ireland.
Football fans in the UK and the Republic of Ireland will be able to watch the likes of Erling Haaland, Jude Bellingham and Robert Lewandowski on Sky Sports.
Sky Sports will show the premium fixture of each weekend at 5.30pm on Saturdays, with further matches broadcasted via Sky Sports' linear or digital channels.