Walcott told BBC Sport: "What's really fascinating is that Mikel Arteta will allow him to do that because that's his strength.
"He carries the ball, he's quicker with the ball. He's like Messi. I remember playing against Messi - when he was off the ball he's not quick. Maybe it's because I was quicker than most.
"When he had the ball he would just glide past people, glide past me with ease. [Dowman's] got that, he's got the stop-start.
"The biggest challenge is the outside noise and how he copes with even his school life, that balance of even walking out on the street and recognising him.
"That social media world, I didn't have that coming through, we didn't have that when we were younger. It was very different."