Neymar sensationally left Barcelona for PSG in the summer in a £200million hostile transfer.
Barca then filed a lawsuit against Neymar over a ‘break of contract’ in a loyalty bonus dispute, only for the player to counter sue.
Relations between the striker and his former club appeared to have hit an all-time low and it was thought Neymar had burned his bridges with the Nou Camp outfit.
But he was pictured back at Barca over the weekend chatting casually with his former team-mates.
And Valverde was asked what he’d do if Neymar wanted to return.
He joked in a press conference: “If Neymar came back? (I’d do) a double somersault with corkscrew!”
Pressed on the serious possibility, the boss added: “We’ll see what happens in the future, but of course I do not want to talk about it.”
Despite Valverde not ruling out a return for Neymar, the deal itself seems unlikely any time soon.
PSG bought the Brazilian in part to boost their global profile as much as improving their Champions League title chances.
Barca complained to UEFA that mega-rich PSG must surely have broken Financial Fair Play rules in order to trigger Neymar’s contract.
But European football’s governing body said their regulations had not been broken.
Meanwhile, Barcelona are preparing for Tuesday’s Champions League clash at Olympiakos.
The players trained today ahead of the game, with a number of first-team stars absent.
Andres Iniesta, Ousmane Dembele, Aleix Vidal, Arda Turan and Rafinha are all absent due to injury, while Gerard Pique is suspended.