Madrid allegedly see the 23-year-old as the long-term replacement for Cristiano Ronaldo and recent reports claimed they had met with the former Santos man ahead of the Ballon d'Or gala in Zurich this month.
Neymar's entourage was quick to deny a meeting with Madrid's representatives took place and, while that has not stopped speculation about his future, Mestre insists he will not leave the club.
"I see absolutely no reason why Neymar would want to leave Barcelona," he was quoted as saying by Marca after their 3-1 Copa del Rey quarter-final second-leg win over Athletic Bilbao on Wednesday.
READ MORE | 'Neymar is very, very, very happy at Barca'
"He is proving to be a great player, a world-class attacker. We are very happy with his performances.
"I don't know whether Florentino Perez watched his game against Athletic, but it is clear that people who like football like a lot of our players.
"For me, Neymar seems very happy here. He has won titles, has made the Ballon d'Or podium, he looks happy to me and I cannot see why he would want to move."
Neymar has a contract with Barcelona until June 2018, but head coach Luis Enrique this week indicated the club are confident the prized asset will soon sign a new and improved deal.