Wilshere, who returned from a 17-month injury absence in October, has been sidelined with an ankle problem since Arsenal's defeat against Tottenham at the start of March.
Walcott has been ruled out since picking up a hip/thigh injury while on England duty in the build-up to last month's World Cup qualifiers.
But while the duo are set to miss this weekend's trip to West Brom, assistant coach Steve Bould is hopeful they could be back to face the Canaries.
"We have good news with both of them," Bould told the club's official website.
"Jack and Theo are outside running and have an outside chance of being involved against Norwich a week on Saturday."
Arsenal, who have won three of their last four league matches, are in fifth place, four points short of a Champions League spot currently occupied by Chelsea.