The Brazil forward signed a new five-year contract until 2021 in October, with his release clause set to rise with each year of the deal.
Neymar, 25, joined from Santos in 2013.
He scored 13 goals as Barcelona came second, three points behind La Liga champions Real Madrid, last season.
Neymar won a third Copa del Rey with the Catalan club last season, adding to two La Liga titles and a Champions League.
Barcelona forward Neymar, 25, has accepted an offer from Paris St-Germain after the French club triggered his £195m release clause. (Esporte Interativo via Daily Mail)
Barcelona's vice-president, Jordi Mestre, has insisted Brazil international Neymar will not leave the Spanish giants any time soon. (Daily Star)
Neymar frustrated at Barcelona and ready for Paris St-Germain move. (Goal)
South American football expert Tim Vickery
There is clearly something there, and if it doesn't happen in this transfer window the speculation is not going to go away in the next window.
Fifa World Player of the Year is an absolute obsession in Brazil. Between 1994 and 2007, five Brazilians won it on eight different occasions.
That set the bar for the subsequent generations. Neymar had seen the degree of difficulty in European club football was going to be strong. So that was the idea of going to Barcelona and being in Messi's shadow - great, pressure off.
But after a while, that shadow stops being refreshing and starts being cold, because you can't be Fifa World Player of the Year if you're not even the outstanding player in your own team.
I think it's absolutely no coincidence that this speculation has emerged shortly after the news that Messi has signed a new contract with Barcelona.
Neymar will not be leaving Barcelona despite reports that Paris St-Germain have triggered his £195m release clause, club president Josep Maria Bartomeu has told BBC Sport.