The Brazilian star wanted to leave Paris Saint-Germain prior to the transfer deadline and was reportedly desperate for a Barca return, though a move did not materialise.
It came just two years after Neymar left Barca for Ligue 1 giants PSG in a world-record €222 million (£198m/$244m) deal.
Neymar's father and agent has already claimed negotiations between Barca and PSG are not over amid ongoing speculation.
Bordas kept the door open, telling EFE: "While he wants to come, we will do what we can to bring him back.
"What happens will happen, everything is constantly changing in football, but Neymar is Neymar.
"The case of Neymar is a special one. He's an exceptional player and he wants to come to Barcelona; he hasn't adapted to Paris; he was wrong to go there, and even he has said that."
It's not just the future of Neymar that has dominated the press with Barcelona's superstar captain Lionel Messi also making headlines.
Messi signed his latest contract in 2017, with the deal running until the end of the 2020-21 campaign.
"I don't see him at another club," he said. "There are few people more connected to Barcelona than Messi.
"Messi is from Barcelona [having moved as a child and spent most of his life there]. Messi is Barcelona.
"People are worried about his contract clause, but Messi will stay because he is at home here, he feels it. He comes from La Masia, you only have to look at him when a match has been lost."
Barca vice-president Jordi Cardoner, meanwhile, added: "We are calm and there is a lot of positivity, especially in the dressing room.
"Leo will do what he thinks is fit, but Leo's contract is very special because he is who he is. It's a concession made to him and other players who deserve it. He can enter and leave the club when he sees fit. I'd love for him to stay for as long as he wants to play for our team."