The Sun says the Gunners legend, 34, had said he hoped to spend another season at Eastlands after helping City win the FA Cup and clinch a Champions League place.
But the midfielder could now decide to hang up his boots.
He said: "When you are at a fitness level where you don't want to be, it's maybe better to retire.
"It's 50-50. Either I'll continue playing for City or do something else."
Vieira is being linked with a role on Arsenal's coaching staff.