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Luiz and Ceballos both stayed with the Gunners during the international break and took part in a training game on Friday.
The Athletic claim Ceballos hit Luiz with a firm tackle, which saw Luiz react by striking the on-loan Real Madrid midfielder in the face.
But the 24-year-old has taken to Twitter and slammed the report, which also claims Luiz's scratch drew blood, as 'fake'.
It is alleged manager Mikel Arteta and other members of the coaching staff had to step in and separate the pair.
Arsenal suffered a 3-0 defeat to Aston Villa in their last Premier League game before the international break and it has been speculated tensions boiled over.
Ceballos has already been involved in a minor confrontation with a teammate this campaign, young striker Eddie Nketiah.
Arsenal were preparing for their season opener against Fulham back in September and the duo took part in a rondo training drill.
You don't see this every day :eyes:
Dani Ceballos and Eddie Nketiah got into a heated exchange during a pre-match training routine :handbag: pic.twitter.com/u1qMPuZ8Ux
- Football on BT Sport (@btsportfootball) September 12, 2020
The Spaniard appeared to lunge towards the 21-year-old who reacted angrily.
It then saw the pair square up to each other before their Arsenal teammates intervened and broke them up.
Meanwhile, Arteta recently sat down with beIN Sports and explained the situation with Mesut Ozil.
Arteta played with Ozil for three years and admitted he was 'hurt' by the situation.
"I'm hurt because I don't like any player in my squad not to have the possibility to participate or to compete, for me it is really sad because I don't think anybody deserves that" the 38-year-old said.
"With Mesut at the moment, with the squad list, obviously he cannot be involved. I try to be as clear as possible with him and with the fans and all the media because they deserve to know the reasons why and some people will understand and other people won't understand it."
Arsenal are currently 11th in the league and face Leeds United on Sunday afternoon.
Featured Image Credit: PA Images
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