Bordas travelled to the French capital with Barca’s sporting director Eric Abidal, CEO Oscar Grau and Brazilian scout Andre Cury for negotiations with Paris Saint-Germain to bring back the club’s former forward.
“There’s still no agreement,” he told a cluster of reports on arrival at Barcelona El Prat airport on Tuesday evening.
“We are negotiating and we are closer, but I can’t say anything more.”
Barcelona have until next Monday to finalise a deal for the 27-year-old attacker, who left the Catalan club to join PSG in a world-record €222 million transfer in 2017.
Neymar arrives in Paris - In pictures
PSG have rejected two previous proposals from Barca: a player-plus-cash offer and a loan deal with a transfer to be made permanent next summer.
With Ousmane Dembele keen to stay at Camp Nou, this last attempt is thought to be a straight money offer for around €170m, although it is unclear when all of that would be paid.
