The Brazilian moved to Camp Nou from Santos in 2013, in a transfer which proved to be controversial.
Neymar's switch saw Barca accused of tax fraud, with former president Sandro Rosell resigning from his post, although both he and the club deny any wrongdoing.
The 22-year-old's current deal is set to expire in 2018, but his representative, Wagner Ribeiro, has claimed the club want to tie the player down for a further two years.
"Of course Barcelona want to renew his contract. Until 2020? Yes," he said.
Speaking at the launch of a project designed to help the disadvantaged in Brazil, Neymar said: "I'm happy in Barcelona. I have a contract there and there's still a lot left for me to do."
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