Barcelona club director Raul Sanllehi has held talks with Neymar's representatives over a move to the Nou Camp, according to the Daily Mirror.
Reports in Spain carried by the Daily Mirror claim Sanllehi met Neymar's agent, Andre Curi, and Neymar's dad Neymar Sr Da Silva in Geneva last week.
The trio held talks over a possible transfer to Barcelona, with negotiations thought to be ongoing.
The Brazil international has been a long-term target for Barcelona, although several of Europe's top clubs, including Real Madrid and Manchester City, have been linked with a move for Neymar.
But reports have emerged in recent weeks of a secret agreement between Barcelona and Santos for a deal for the Brazil international, and these latest claims regarding the Geneva meeting suggest a transfer is inching ever closer.
The prospect of Neymar and Lionel Messi in the same team is mouthwatering, and would make Tito Vilanova's side the automatic favourites for the Champions League next season.
The La Liga leaders could be extremely active in the transfer market this summer, with the same Daily Mirror report quoting an article from Catalan newspaper Mundo Deportivo that claims that the Spanish club have drawn up a five-man Premier League shortlist.
Jan Vertonghen, Thomas Vermaelen, Daniel Agger, David Luiz and Vincent Kompany are all under consideration, as Barcelona look to bring in another central-defender at the end of the season.