The 19-year-old has emerged as one of Brazil's brightest young prospects in recent years and has long been linked with a move to Spain's big two.
Premier League sides Chelsea and Manchester City have also been linked with the Santos striker, who played for Brazil in their 1-0 friendly win over Ghana at Craven Cottage on Monday.
Speaking after that game Neymar admitted that Barca and Real are interested in him, but stressed that no deal had yet been agreed.
"Real Madrid and Barcelona have come calling for me. Both clubs want me," he told AS.
"I can confirm it, but I have not reached an agreement with any of them.
"The interest from Spain's big two means that my self-esteem is very high because I am being followed by two big clubs like these."
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