The former Gunners forward, who scored 185 goals during his time at the club, believes that Walcott has the ability to succeed in a new position.
Wright told ESPN: "I love Theo and have been saying for a long time that he should be playing as a striker.
"Clearly he is not the finished article and could do with some more work from the Arsenal coaches, but Theo has all the ingredients to be a top striker.
"Wenger has been saying for a long time that he sees Theo developing into a striker, so give the guy a chance to prove he can do it. If it doesn't work, then fair enough, but give it has to be worth a try."
Following Walcott's brace in the victory over Coventry City on Wednesday, Wenger hinted he would give the 23-year-old a chance as a striker in the future.