Speaking at a news conference to reveal Barcelona's financial results and record revenues of €708m over the last 12-month period, Vives insisted Neymar remains committed to work under new head coach Ernesto Valverde and that any sale would be unimaginable. "He played a magnificent season and he is still one of the best in the world".
And, according to Sport, Neymar is giving more thought to a move away from Catalonia than ever before.
The report adds that those close to Neymar have told him that "by the side of Messi you will always be second, you will always be in his shadow".
Europe's biggest teams, including Manchester United, Manchester City, Paris-Saint Germain and Real Madrid, remain interested in signing the former Santos attacker, who has scored 105 goals in 186 appearances for the La Liga side.
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The 33-year-old midfielder - who made just 13 starts in LaLiga last season - has regularly indicated he wants to retire at Barca, but Valverde is not concerned that Iniesta is now in the last year of his contract. His release clause this summer stands at €200m, while it will steadily increase over the next three years eventually up to €250m.
The 25-year-old is preparing for his fifth season at the Nou Camp, and despite displaying how devastating he can be alongside Lionel Messi and Luis Suarez, coupled with the countless trophies and accolades that they've collected together, the same reported problems persist. "Neymar is part of an attacking trio that bears no comparison in world football".
Manchester United manager Jose Mourinho wanted the Brazilian to replace Zlatan Ibrahimovic, while Neymar has admitted previously that his representatives have been in touch with PSG.