Despite his current deal not being set to expire until the summer of 2018, the Blaugrana are keen to tie him down amid fresh reports he could be tempted away.
On Monday the Brazilian claimed the award for La Liga's Best South American Player for 2014-15 while he has continued to excel this season to earn a place in the final three for the Ballon d'Or.
After recently saying himself he wants to extend his current contract, his father Neymar Snr, who also works as his agent, has promised that the 23-year-old will remain at the Nou Camp.
"Stay calm, I'm sure Neymar will renew," he told Marca. "There is no hurry. He still has three years on his contract."