While he missed this week's 35-man squad, England coach Thomas Tuchel has stated the door is still open to the 16 year-old.
Former Arsenal winger Walcott, who was selected by England as a 17 year-old for the 2006 World Cup, says it would be the worse thing for Dowman's career to make the final cut.
He explained to the Mirror: "I hope he (Dowman) doesn't go. I don't mean it in a horrible way because if I could go back in time, I would change things. "I would say to myself: 'No, no, don't do it' but then try telling that to a 17-year-old!
"I do still see him and me differently as he's playing in the Premier League but he needs to grow at his own pace, especially on the emotional side because he's a young adult.
"I had to grow up very fast but this team is still young and not as experienced. He's being protected, which is important, whereas I had to get thrown in to talk to you lot!
"In time he will go, yes, but I don't think this is the time and I think there are better players who arguably deserve to be there ahead of him.
"He will eventually get there but England have wide players doing really well, there's Bukayo (Saka), (Noni) Madueke, Jarrod Bowen and Anthony Gordon and Harvey Barnes on the other side."