Wilshere, who only returned from a 17-month injury-enforced lay-off in October, has been out since the 2-1 defeat by Tottenham on March 3 because of an ankle problem while Walcott has been sidelined since incurring a hip/thigh injury while on England duty in the build up to last month's World Cup qualifiers against San Marino and Montenegro.
The pair will miss Saturday's trip to West Brom, but Arsenal assistant coach Steve Bould revealed on the club's official website: "We have good news with both of them. Jack and Theo are outside running and have an outside chance of being involved against Norwich a week on Saturday."
Wilshere's likely return will be welcomed by Arsenal as they step up their push for a top-four finish, with three wins in their last four Premier League matches renewing hope of qualifying for the Champions League.
If the 21-year-old midfielder features against Norwich, he will have missed four matches for the Gunners and the England double-header.
Spanish left-back Nacho Monreal is available against West Brom this Saturday after recovering quickly from the knee injury suffered in last Saturday's 4-1 victory over Reading.
Source: PA
Source: PA