The new deal will see Neymar become the world’s third-highest paid player, earning £500,000 a week at Barcelona.
Barca president Josep Maria Bartomeu said: “This is the season we will sort out a new deal with Neymar.
“But we will try not to talk about the negotiations and to work discreetly until we can announce it.”
Barcelona will hold talks with Neymar’s dad over a new deal before the January transfer window opens.
Neymar was strongly linked with a move to Manchester United over the summer.