Earlier on Monday, Barca technical director Robert Fernandez insisted the La Liga giants had received no offers for its players this close-season and maintained no one was in the market to meet the release clause inserted into Neymar's contract when he signed fresh terms running until June 2021 last October.
Nevertheless, suggestions that PSG were ready to make a sensational transfer move persisted, with Catalan sports daily Sport claiming Neymar's advisors believe it is time for the 25-year-old to step out of Lionel Messi's shadow at Camp Nou.
Madrid paper AS reported Neymar's father will travel to Paris to discuss the blockbusting move with PSG owner Nasser Al-Khelaifi this week, the Ligue 1 club being prepared to use Italy midfielder and Barca target Marco Verratti as bait.
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.
"The only thing we care is he keeps being happy here," Vives said. "He played a magnificent season and he is still one of the best in the world.
"He is happy in the club and the club is happy with him. He verbalises it and he shows it with his attitude. We are relaxed about that and we only hope next season is better than the last one.
"Neymar's departure is not in club's imagination; the club just thinks of keeping the best players like him, one of our main symbols."
Neymar - who starred with a late brace in the improbable comeback to beat PSG 6-5 on aggregate in the Champions League last season - was included alongside Messi and Luis Suarez in a strong Barcelona squad that will face Juventus, Manchester United and Real Madrid as part of the International Champions Cup in the United States.
Gerard Deulofeu, who recently returned to his boyhood club from Everton, is not in the travelling party due to an abductor problem, while Rafinha is continuing his rehabilitation from knee surgery three months ago.