Arsenal star Walcott will face Bale and Tottenham this weekend.
Woodward was director of football at Southampton when the club's academy team really blossomed in 2005 and 2006.
He told The Sun: "Whatever the sport, you can see potential greatness in individuals even when they are just kids.
"Gareth and Theo were just that, kids, when I was at St Mary's but their quality was evident even then as 16-year-olds.
"Gareth was a flying left-back, Theo a striker or winger. They both had obvious talent and were very exciting to watch.
"And it helped them greatly to be part of a tremendous academy side. If you look at that squad, you'll find players, the vast majority of whom are in the Premier League or Championship today."