The winger burst onto the scene at Southampton at the age of 16 but he soon secured a transfer to Arsenal in an attempt to fulfil his potential on both the club and international scene.
Walcott, now 27, has enjoyed an above-average career at the Emirates Stadium, netting 84 goals in 336 appearances in all competitions and he has scored eight times in 42 matches for England.
However, his form at the Gunners has dipped in recent weeks and he faces a fight to make it into Roy Hodgson's 23-man squad for Euro 2016, which takes place in France during the summer.
Walcott only extended his existing deal at the North London outfit last year, but Wilkins feels that it his time for the attacker to leave the club at the earliest opportunity.
Wilkins said: "He has been there for 10 years now and played 225, 226 games in the Premier League. That's not enough. I think it is time that Theo moved on because he has to play games. He has not played near enough football.
"I think it could be on the cards. Time to move on, time to start playing some football because if he hopes to get where we think he can get, then he needs to be playing."
After recovering from a serious knee injury, Walcott has gone on to make 22 appearances in the league this season and a further 12 in all competitions, but he has been used from the bench on various occasions and the form of Alex Iwobi is threatening to keep him there on a regular basis.