The pair were seen exchanging words on the pitch as they argued over who would take a penalty during their 2-0 win over Lyon on Sunday night, with Cavani winning the dispute but then failing to put away the spot kick.
According to various reports, the strikers then came to blows in the dressing room and had to be kept apart by teammates.
While Cavani has insisted that he has "no problem" with the Brazilian, Spanish publication Sport today claims that Neymar has told PSG president Nasser Al-Khelaifi that "his coexistence with Cavani is totally impossible".
The newspaper adds that Neymar - a world-record £200m signing from Barcelona - has asked Al-Khelaifi to now sell the 30-year-old, who has been at the Parc des Princes for more than four years.
Neymar has yet to officially comment on the incident, although he is said to have unfollowed Cavani on Instagram in the wake of the incident.