It is understood that N'Zogbia, 22, took exception to a late challenge by the 6ft 3in forward and fists flew until their fellow players intervened and the work-out was quickly abandoned.
N'Zogbia has admitted he wants to quit the Tyneside club and the fracas at Newcastle's Darsley Park training ground will do little for morale at the club where relegation worries are mounting following a run of just four wins in 16 league games since Kinnear took over.
It was played down as a "minor incident" by a Newcastle insider who added: "It was nothing more than handbags at ten paces. It is the sort of thing that probably happens on training grounds all the time and should not be blown out of all proportion."
The fight broke out shortly after the Football Association had charged Kinnear and Hull's Phil Brown with improper conduct following their touchline bust-up during an FA Cup tie a week ago.
It could mean a lengthy touchline ban for Kinnear because he already has two charges hanging over him and his previous actions will be taken into consideration when FA officials evaluate his latest brush with the authorities.
'They could throw the book at him this time,' an FA source said. 'They will take into account his past behaviour so he can not expect to get off lightly.'
Kinnear, who served a long-standing two-match touchline ban when he arrived at Newcastle, was warned by the FA about his behaviour in October following a foul-mouthed rant at newspaper reporters.
A month later he landed himself in hot water with the FA by branding referee Martin Atkinson a 'Mickey Mouse official' following Newcastle's 2-1 defeat at Fulham and was charged with improper conduct.
He was sent to the stands by referee Mike Riley in the closing stages of a 2-2 home draw with Stoke last month for allegedly hurling abusing at one of the official's assistants and charged with 'using insulting and offensive'.
Kinnear has denied the latter accusation and has requested a personal hearing. He may also choose to deny the latest allegation, having blamed Brown for the altercation, and the pair have been given until Feb 3 to respond.
Brown is no stranger to the game's governing body and received a £1,000 fine and a warning about his conduct after kicking a water bottle that struck a fourth official during the 5-0 defeat by Wigan last August.
Former Nottingham Forest manager Colin Calderwood has denied suggestions he is set to become part of Kinnear's backroom staff. 'If I have been appointed as coach of Newcastle United then that is certainly news to me,' he said. 'I don't know anything about this.'