The 22-year-old England international is one of several big names who could be heading for the Emirates Stadium exit door, as the Gunners boss prepares to launch a major rebuilding project in north London in an attempt to end the club's search for silverware - now set to go beyond a seventh season.
Walcott has failed to hit the heights that his early promise in an Arsenal shirt suggested, and has deservedly come under fire from fans after a series of under-par performances this year.
According to reports in today's press, the tricky winger could be offered the chance to revive his career at Premier League rivals Chelsea, who are ready to make a move for the former teen prodigy as Andre Villas-Boas undertakes a rebuilding project of his own at Stamford Bridge.
With a little over a year left to run on his existing contract, it could be time for Wenger to cut his losses and sell Walcott this summer, or risk losing him for nothing in 12 months time.
After a limp display in the 4-0 defeat away at AC Milan in the Champions League last week, Walcott was substituted unceremoniously at half-time and has not featured for Arsenal since their San Siro mauling.
In the aftermath of the game, former Gunners midfielder Emmanuel Petit was particularly critical of Walcott, claiming he and a number of other young players have failed to repay the faith shown by Wenger, and called for those underachievers to be sold.
"In midfield there isn't anything now, the defence is constantly under construction," he told French website sofoot.com. "Certain young players haven't done enough to justify the confidence that Arsene has in them.
"Walcott — somehow he's going to have to reach the next stage. It's been years that he's been at the same level."
The emergence of Alex Oxlade-Chamberlain - who followed a similar path to Walcott, arriving in north London from Southampton - has cast further doubt over whether the England winger is even worth a starting place in the Arsenal side. The under-fire star is no stranger to criticism however, and in an interview last month he confessed that his recent performances had been below par.
"I don't pay any attention to it. I just want to play my game and show people what I can do," he told the London Evening Standard. "I am the best judge of my performance, not anyone else.
"I wasn't happy with my last few games but, hopefully, now I can try to get back to a level I should be at. Everyone should realise I am a good judge of my character."
On a creative level, Walcott has certainly stepped up to the plate, having established himself as a vital influence for Arsenal this season, providing seven assists in the Premier League - a joint-club-high along with Robin van Persie - a figure only five other players in the whole division can better, with no other Englishman able to match that impressive haul of assists.
However, despite possessing blistering pace, Walcott's dribbling success is surprisingly poor. Of the 86 dribbles undertaken in the league - the 10th highest total - he has only beat his man on 30 occasions. That equates to a completion rate of just 35 per cent - the fifth-lowest rate of any player to attempt 20 or more dribbles this season according to Opta stats.
A lot has been said about Walcott's natural central striking instincts, but judging by his scoring and shooting stats this season, he's not yet ready to lead the line for Arsenal.
With only three Premier League goals to his name this season, at a rate of one every 627 minutes, it's clear that there is still plenty of room for improvement.
What's certain is that Walcott will continue to divide opinion, but while he may still struggle in front of goal, he does provide a vital creative threat going forward - a key ingredient for any successful team.
If Wenger fails to persevere with the development of his chance maker, come chance taker, then Arsenal's loss could turn out to be Chelsea's long-term gain.