Paris St-Germain have reportedly triggered the forward's 222m euro (£199m) release clause, although Barca president Josep Maria Bartomeu told BBC Sport the 25-year-old is not for sale.
Neymar did not speak to reporters after the pre-season win in New Jersey, but Valverde did address the speculation.
"We want Neymar with us," he said.
"We know his value on the pitch and what he brings to the locker room."
Neymar, who joined from Santos in 2013 and signed a new five-year contract until 2021 in October, only played for the first half of the International Champions Cup contest.
He opened the scoring after 15 minutes following a clever exchange with Paco Alcacer and doubled the lead nine minutes later, drilling low past Gianluigi Buffon after burrowing through the Juve defence.
Giorgio Chiellini scored a consolation for the beaten Champions League finalists just after the hour in front of a sell-out 82,104 crowd at the MetLife Stadium.
PSG coach Unai Emery would not be drawn on the speculation following his side's International Champions Cup opener against Tottenham.
After the Premier League runners-up recorded an emphatic 4-2 win in Orlando, Emery would only say PSG are "always looking for players who can help the team" when asked about Neymar.
Christian Eriksen and Eric Dier cancelled out Edinson Cavani's opener in front of 33,332 fans at the Camping World Stadium, before Javier Pastore pulled PSG level just after the half hour.
However, PSG goalkeeper Kevin Trapp was sent off in the opening 20 seconds of the second half for handling outside the box and Spurs capitalised with further goals by Toby Alderweireld and Harry Kane.
"There are lot of positives to take," Spurs coach Mauricio Pochettino said. "It's a friendly but playing this kind of team it's always good to compete."
Coach Ernesto Valverde reiterated his desire to keep Neymar at Barcelona after the Brazilian scored twice in a 2-1 friendly win over Juventus.