The Frenchman is the top target for title-rivals, Real Madrid but Valverde is confident that he can convince him for a move to Camp Nou.
Slowly, slowly, on a day by day basis, Neymar's enormous move to PSG moves ever closer to possibly happening.
Barcelona now face a tough task of replacing the forward and have set sight on Mbappe.
However, Neymar has moved to deny such speculation, stating that the last one was his best season in Barcelona.
This situation is similar to Kobe Bryant and Shaquille O'neal's case where Shaq was the undisputed No. 1 and Kobe wanted to be the world's best, but the dominant center overshadowed Bryant with his overpowering style of play.
'If he comes, he'd be an exceptional player, who would help us a lot'.
Barcelona are said to be already tired of the incessant Neymar to Paris-Germain drama every summer. But is there any substance to them?
Bartomeu's comments echo those of club vice-president Jordi Mestre and spokesperson Josep Vives, who both said earlier this week they were confident Neymar would not leave the club. This quest is not easy.
PSG are offering an incredible contract and Neymar will be the leader and star of the Ligue 1 side.
Paris Saint-Germain are preparing to hold talks over a world-record €222m (£196m) deal to buy Neymar from Barcelona.
On the eve of the information appeared about the readiness PSG to pay Barcelona prescribed in the contract of Neymar 222 million euros. Neymar told the PSG players he "will join them at his new club", according to the report. There's nothing we'll ever do off the field that could beat that moment.
And for that to happen, either Neymar or Alexis Sanchez could easily become the missing piece of the club's puzzle for the 2017-18 campaign.