The Uruguay striker was booked after a clumsy tackle on the Brazil captain during last week's meeting at Emirates Stadium, leading to an exchange of opinions between the two forwards.
Their PSG colleague Kylian Mbappe insisted there will be no problems when they reconvene after the international break, sentiments echoed by Cavani.
"The things that happen on the field is football, but after that we are friends, brothers, team-mates," Cavani said. "But during the match you want to win, that's normal and you defend your team.
"I did not do anything, I did not touch him, I went to see him and told him that I had not touched him, only that, but I did with him as I would have done with another.
"There's no need to talk about it, there's nothing, it's the media talking about it."
Cavani was also asked about the destination of the Ballon d'Or, which he feels should go to a Frenchman after its World Cup win at Russia 2018, which included a quarter-final victory over Uruguay.
"Three or four players deserve it," said Cavani, who missed that match through injury. "[Raphael] Varane can be one of two, three, [Antoine] Griezmann...Kylian, he's been doing good things for two years.
"You have to look at each other's performance, not just the name. Watch the last years, what everyone has done, the titles won, the seasons made.
"For me, it's a Frenchman who has to win. There are other players, but it must be a Frenchman. [Luka] Modric has had a great season but Varane has won the Champions League [as well]. Okay, Modric is a [World Cup] runner-up and had a great season, but Varane deserves it more."