"I hope I will sign. I will have a meeting with the [vice-]chairman [David Dein] on Monday or Tuesday and I hope that will be the last meeting," the French midfielder, who has had protracted contract negotiations with the club, said on Friday.
"The money is sorted out. As I said, on Monday or Tuesday I hope everything will be sorted out."
Arsenal are sweating on whether both Vieira and his midfield compatriot Robert Pires will sign new contracts. Pires is also yet to agree to a new deal.
The nightmare scenario for Arsenal is that both players decline new deals and are then eligible to leave on free transfers when their contracts expire.
"We said we wanted to finalise everything before we start the Premiership season [next Saturday]," said Vieira, who should start for Arsenal in Sunday's Community Shield game against Manchester United.
"I hope I will sign by Saturday. If not I will stay for the year left on my contract."
