However, PSG president Nasser Al-Khelaifi said on Saturday he was "2000 per cent" sure the Brazil international would stay at the club.
Emery, who leaves the club after two seasons in charge, also feels Neymar will remain at PSG.
"This season there have been times when everything related to Neymar was oversized," he told Cadena SER.
"Neymar is not talking much. He told us he was tired of the lies that are told.
"I'm not going to be Neymar's spokesperson, but I think the next season he is going to stay at PSG. It would be the right thing for the player and for the club."
Neymar scored 28 goals in 30 games in his first season at PSG, but a serious foot injury in February saw his campaign ended prematurely.
Emery believes the star forward was on track for his best season yet before his injury.
"I have really enjoyed Neymar. I was very happy with him. He is at the level of Cristiano [Ronaldo] and [Lionel] Messi," he said.
"The injury has hurt him because he could have gotten his best numbers. I am convinced he will reach the maximum level."