Ben Arfa joined the Ligue 1 club in January after his Newcastle United contract was terminated by mutual consent following a spell on loan at Hull City.
The 27-year-old did not feature for Newcastle's first team this season, but did play in an Under-21 game for the Tyneside club and the LFP deemed that to count as a competitive fixture so Ben Arfa was left in limbo as FIFA rules state players can appear for no more than two clubs in a season.
LFP last Friday ruled that Ben Arfa would be unable to feature for Nice in the current campaign.
Ben Arfa's lawyer suggested his client could contemplate quitting, but, while Ben Arfa is not planning to hang up his boots just yet, the former Lyon man said his goodbyes at a news conference on Tuesday.
"It's finished with Nice. I am very sad, I wanted to bring something to Nice," explained Ben Arfa.
"I'm sad, but I do not want to dwell on it. To play football, I would go to the North Pole.
"Give me time to digest it all, then I will talk about my future."
Ben Arfa also revealed that he could opt to continue his career in other country.
He said: "The objective is to find the competition, and therefore may go abroad."
Coach Claude Puel added: "If Hatem wants to return, to train, to greet us, he will be welcome."
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