The exchange with Witsel reportedly came during Dortmund's 1-1 draw with Augsburg last time out, as good as ending Bellingham's trophy hopes for the season.
Dortmund are now eight points behind Bundesliga leaders Bayern Munich with 10 games to go, and have already exited the Europa League and German cup.
Dortmund began the season in the Champions League, but a third placed group finish saw them drop down into the Europa, which they soon departed at the hands of Rangers.
Bellingham was the star of the show at Ibrox in the last 32 clash, with his side trying to overcome a 4-2 first leg deficit, only to draw 2-2.
The 18-year-old had little help from his teammates during the draw, and lost his cool at left-back Nico Schulz after a misplaced pass.
Bellingham's reaction was picked up on camera, with Sport1 reporting he said: "You can't get one f* pass off, you're f* s. Every f*** time!"
His manager, Marco Rose, defended the outburst, claiming the anger shown is what his team needs more of.
"Where Jude comes from, you possibly speak a bit more rough in English," Rose said.
"That's part of it. Jude wants to win games, he's angry - and that's part of him as a player and something we actually need even more."
However, in the next match there was another awkward scene with Bellingham furiously reacting to fellow midfielder Witsel, as Dortmund failed to collect three points against Augsburg in their pursuit of league leaders Bayern.
The former Birmingham midfielder was seen waving his arms in anger at a player 14 years his senior, and things then reportedly carried on into the dressing room.
German outlet Sport1 claim that Witsel wanted to correct Bellingham's runs forward, but had his attempts turned away by the teenager.
"That's going way too far," said Sport1 chief reporter Patrick Berger. "He splits the room with his behaviour.
"That doesn't go down well with the team. With his demeanour, he's starting to annoy even the experienced players.
"This is a delicate situation. He performs, but on the other hand an 18-year-old has to rein himself in.
"There is also the question of who will intervene in the dressing room. That is currently missing."