The Brazil forward is expected to move this summer despite talk over an extension to his current Santos contract, which expires in 2014.
Manchester City, Chelsea and Real Madrid, along with Barcelona, have all been linked with Neymar and Santos are aware of all the interest.
But the club are not putting the 21-year-old under any pressure, with vice-president Odilio Rodrigues telling La Xarxa Radio: "Barcelona are a great club with excellent players and they would be good for Neymar.
"We are aware of the interest in the player. But there are other clubs interested. It will be Neymar's decision."
Rodrigues, in an ideal world, would like Neymar to stay at Santos but he knows the spending strength of Barcelona and Real will make that difficult.
He said: "Santos want the player to stay at least until after 2014. But we know it is hard to compete with the economic power of the Spanish clubs."