The 21-year old's future has been the subject of speculation for a number of years since coming through the ranks at Santos and establishing himself as a key part of the Brazilian national team.
Neymar has attracted interest from across Europe, but Rodrigues says that a move to Barcelona is the player's preference.
"Neymar has told us he wants to sign for Barcelona," he told Ser Esports.
"There are other proposals but he has preferences for Barca. There is no official Madrid proposal for Neymar but we know that this offer will come.
"We held conversations in Spain with the Barca board of directors and there are on-going talks but nothing has been decided.
"But the negotiations need to continue because the first bid we were offered was not enough. We know that Madrid had a bid and will be presenting it soon, but I haven't talked to (club president) Florentino Perez.
"We know that the athlete's opinion is important. What we have to do is to find a way to unify the best offer with the player's interest."
Neymar has been a regular fixture in Luiz Felipe Scolari's Brazil squads and the former Chelsea boss was full of praise for the youngster.
"He is an example to follow as a sportsman," he said to Canal+.
"I have spoken to Sandro Rosell about how he behaves on the training pitch and about his personality and he really is an example to follow.
"Barcelona are clearly leading the race for his signature. He would be a great signing for Barcelona.
"He would be an idol for the fans next season alongside Lionel Messi."