In a statement sent to Sky Sports News, the French midfielder said Kinnear had insulted him, although he did not elaborate on how.
Kinnear responded by accusing N'Zogbia of trying to engineer a move away from the struggling Premier League club.
"First of all I wish to apologise to the fans for wanting to leave the club," N'Zogbia's statement read.
"However, having been insulted by Joe Kinnear, I will never play for him again while he remains Newcastle manager.
"The club are aware there are offers on the table and they should accept one of them."
Kinnear mispronounced N'Zogbia's name during a post-match television interview after the 2-1 defeat by Manchester City on Wednesday - appearing to pronounce his name 'Insomnia' - but said he was surprised if the 22-year-old had been insulted by that.
"I couldn't believe it when I was told Charles had issued a statement claiming he was insulted, apparently for nothing more than me mispronouncing his name in a post-match interview at Manchester City," Kinnear said in a statement issued through the club.
"Ok, I got a little tongue-tied, but if I had a pound for every time I've mispronounced a player's name down the years then I'd be a very wealthy man indeed.
"There have already been plenty of quotes attributed to Charles during January saying he is interested in leaving for other clubs but the truth is we haven't received a formal offer for him.
"Sadly this just smacks of a desperate attempt to engineer a move away from Newcastle United -- a club that gave Charles the chance to play in the Premier League and which has rewarded him handsomely during his time at St. James' Park."
N'Zogbia, signed from French club Le Havre in 2004, did not feature in Newcastle's squad on Wednesday and has been linked with a move to several Premier League clubs in the transfer window.
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