Reports have suggested the Brazil star has become unhappy in Paris, even perhaps regretting leaving Barcelona for the French capital club in a move that made him the most expensive player of all time.
Additionally, Goal revealed that Neymar has a gentlemen's agreement with the PSG board which will allow him to leave for Madrid should he help deliver Champions League glory to the Ligue 1 champions.
Emery, however, insists his star attacker is going nowhere.
"He is happy on the pitch and with his team-mates," the Spanish coach said.
"He will become the best player in the world. That is for sure. But he will do so here."
Emery will have to cope without Neymar in the short term, though, as the Brazilian contends with a minor injury. Fellow forward Kylian Mbappe will also miss PSG's upcoming clash with Montpellier.
"[Neymar has] a minor injury,” Emery continued. “However, he needs to feel 100 per cent before he can play again. Yesterday, he felt good [in training]. I hope it will be the same later.
"We need to be patient with [Mbappe]. I do not think he will be ready for Montpellier.”
In addition to the absences of Neymar and Mbappe, Emery confirmed that surprise new signing Lass Diarra will require “one or two weeks” before he is match fit and ready to compete, while Dani Alves continues to serve a ban – much to the coach's chagrin.
"His three-match suspension is totally unfair,” the boss concluded.
PSG's clash with Montpellier kicks off at 1600 UK time on Saturday, with Parc des Princes the backdrop for the Ligue 1 match-up.