The former PSG, Caen, Monaco and Bastia player, who won 13 caps for France and now works as a pundit for RMC Sport, said Dembélé and those close to him had reacted with real anger after Mbappé suggested in an interview with France Football that he had always been seen as "the chosen one," while Dembélé had merely been viewed as talented.
"Dembélé took it very badly, that's for sure, he's very angry with Kylian Mbappé," Rothen said. "For him, it's a form of betrayal. The words are strong, but that's exactly how it's being seen. And it's not just him. It's everyone around Ousmane, the people who are with him in the PSG dressing room. His France teammates too."
Dembélé, the reigning Ballon d'Or holder, waited several days before responding, doing so on television following a PSG win. "I've always been at the back of the class working hard," he said. "Throughout my whole career I haven't said a word; I've worked extremely hard.
"As I've said, I was never seen as the chosen one, but I put in the effort and last year I was rewarded with a fantastic season at PSG. This year, we'll see - no pressure, nice and calm."
Rothen suggested the fallout could complicate life for incoming France coach Zinedine Zidane, warning that a number of players privately side with Dembélé rather than Real Madrid star Mbappé despite representing the same national team.
"People tell me there are plenty of France players who, once again, don't understand all of his comments, and who are more in Dembélé's camp than Mbappé's, even though it's the same squad," Rothen said. "But apparently there are now two camps."
He added that Dembélé has traditionally played peacemaker within the France squad, making the timing of this dispute particularly awkward.
"Ousmane, who is far more conciliatory than Kylian, has often acted as a mediator between players in the France squad," Rothen said. "I'd love to be a fly on the wall for the handshake between the two of them at the next international break. I think the walls will shake a little."
Rothen went further, suggesting the World Cup earlier this year had already exposed underlying tension around Mbappé's conduct, even as his performances on the pitch as top scorer helped mute criticism at the time.
"The feeling we had at the World Cup is even more obvious today," Rothen said. "Plenty of players had issues with Kylian Mbappé's behaviour and comments, that's the reality. He's alienated a lot of people within the France squad. The World Cup went the way it went, so it's true that when you finish as top scorer and behave impeccably, as Kylian did at the tournament, that softens a lot of the criticism within the group. But this kind of comment will hurt him."