The Argentina international suffered the injury while on duty for his country in their World Cup qualifier against Peru on 10th September.
Gutierrez will fly back to the North East of England at the start of next week to work with the Magpies' medical team.
Chris Hughton: "It's just a process now, not a matter of days, unfortunately, but I'm hoping it'll be three or four weeks from when he suffered the initial injury.
"He comes back early next week to maintain what he's done so far and to carry on his rehab. It's his right clavicle that he's cracked, but he hasn't had an operation."