The Brazilian centre-back has been linked with a move to Catalonia this summer as Blaugrana look to strengthen their defensive options.
"Any player dreams of playing for Barcelona, but I am very happy at PSG at the moment," the 18-year-old told Globo Esporte.
"There was speculation and talks with Barcelona last year but unfortunately they didn't continue, nothing has come this year and I am very calm regarding these transfer related things.
"I have always wanted to play for a big club in Europe and thank God I have achieved everything I wanted to in my life, at both a personal and professional level, as I fought hard to get there."
Silva joined Les Parisiens from AC Milan for €42m (£36m) last summer.