France have one match remaining during the international break, with Zinedine Zidane's side facing Belgium on Monday night after already beating the same opponents 1-0 last week.
Olise has once again impressed during the international window and is increasingly viewed as one of the leading figures in Zidane's plans for the future.
The Bayern Munich winger has also established himself as a quiet leader within the squad, according to L'Equipe, although his approach is not necessarily compatible with every teammate.
The report claims Olise has struggled to understand some of Cherki's behaviour, particularly during training. The Manchester City midfielder is regarded as more playful and unpredictable, while Olise has a far more demanding approach to football.
The difference is particularly noticeable because both players are expected to become important figures for France over the coming years.
Olise is described as calm away from the pitch and not especially vocal, but he takes responsibility through his performances and has a very clear understanding of what he expects from the game.
L'Equipe reports that this is an area where he does not compromise.
“Olise has a very precise vision of what the game demands. And he does not like those who get in its way,” the French publication wrote.
That attitude helps explain why the winger has developed into an important player for both Bayern and France, but it has also created a contrast with Cherki.
Cherki has not enjoyed the same impact during the international break. Zidane has used him in a deeper role than he normally occupies, and the 23-year-old has not completely taken the opportunities presented to him by the new France coach.
Olise, meanwhile, has continued to strengthen his position within the team and appears increasingly certain of a major role in the years ahead.
The relationship between the two players will therefore be one for Zidane to manage. Both possess the technical quality to become central to France's next generation, but their contrasting personalities and approaches to the game could require careful handling.
For now, the issue appears to be a difference in outlook rather than a serious dispute, but Olise's inability to understand some of Cherki's behaviour is an interesting detail as Zidane continues to shape his France team.