Assistant manager Steve Bould has confirmed that the two injured Gunners have returned to training and revealed when they could potentially return to competitive action.
The duo has definitively been ruled out for this weekend's trip to the Hawthorns to face West Brom, but still could arrive back in first team ahead of schedule should they recover fitness in time 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."
Walcott has been on the treatment table since receiving a knock while on international duty with the Three Lions prior to the World Cup qualifiers with San Marino and Montenegro. Wilshere hasn't seen action since picking up an ankle injury in Arsenal's 2-1 loss to Tottenham on March 3.
Arsenal currently sits two points adrift of the Premier League's fourth and final Champions League place having won four of its last five games in all competitions.