The 25-year-old Brazil international has insisted he's happy at Barcelona, but the French club could be set to test his resolve by triggering a €222 million release clause in his contract.
Paddy Power still have the Catalan club as 8/15 (1.53) favourites to retain his services this summer, but PSG are now a 6/5 (2.20) shot to complete any potential deal by 1st September.
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That is a significant move from the 25/1 (26.0) available with the same firm just two weeks ago.
The changing of such a market isn't a guarantee of a transfer becoming a reality of course, far from it, but the fact that there is the option to back Neymar to stay at 8/15 (1.53) means that the prices should be more representative of the situation than if there were only options to back a move away from Barcelona.
Having signed a new five year contract at the Camp Nou in October 2016, the forward seemed to be one of the men most likely to remain at their current club throughout the summer transfer window but the reaction from the bookmakers certainly suggests there has been some substantial support for a switch to Paris.
Jordi Mestre, Barcelona vice-president, has rubbished any rumours around the subject, insisting he is "200 per cent" sure Neymar will remain in the Catalan capital but if the Ligue 1 club have indeed bid the amount of money that would trigger the release clause, it would be down to a negotiation between the player and his potential new club, and out of Barca's hands.
PSG recently completed a move for former Barcelona player Dani Alves, who had looked likely to join former boss Pep Guardiola at Manchester City before seemingly changing his mind at the last minute.
The next big question will be, will Neymar follow suit and head to the French capital in a deal that would set an eye-watering new record transfer fee?
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