The Brazilian superstar is a target for the Spanish giants despite only moving to the Ligue 1 leaders in a £198m move from Barcelona last summer.
Speaking at a press conference on Tuesday, he said, per Goal: "Neymar has a future at PSG".
They say Neymar's old side Barca are the Brazil international's first choice if he leaves PSG this summer.
Earlier, they met Neymar at his mansion in Mangaratiba, near Rio de Janeiro, where the 26-year-old is recovering from surgery to fix a fractured fifth metatarsal in his right foot.
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The increasing media pressure has reportedly forced PSG owner Nasser Al Khelaifi and sporting director Antero Henrique to pack their bags and fly over to Brazil to have a face-to-face chat with their biggest star.
Al-Khelaifi said Neymar is "very happy, really motivated and enthusiastic about the idea of returning as soon as possible".
A return to Barcelona has been mooted while Real Madrid have also been linked with a blockbuster swoop for the South American but it seems Neymar also has options to come to the Premier League.
"I don't know where that has come from", Valverde told reporters on Friday. He is also in a race against time to be fit for the World Cup in Russian Federation, which begins on June 14.
Brazil national team doctor Rodrigo Lasmar has previously said that €222 million man Neymar will need at least two and a half months, perhaps three, to be back in action.
Al-Khelaifi echoed Neymar Snr's sentiments and wished his star investment a speedy recovery from injury.