The 18-year-old has recently been watched by scouts from Liverpool, Manchester City, Arsenal and Juventus.
Neves, who is managed by agent Jorge Mendes, has been hailed as the next big talent in Portuguese football.
Da Costa said: “Ruben has a contract until 2019 and not until 2017, as sometimes I see in reports.
“And we would like to keep him at FC Porto, as a kind of Joao Pinto. That is, he was a symbol and legend of the progress of the club for several generations.
“I never want him to leave Porto. Since I want him to stay for a long time he can be Porto’s greatest captain.”
