Cole, who was hailed as a world-class talent during his early years, is wary of expecting too much from Walcott so early in his career.
"We have to remember that he's still only 19 and there shouldn't be too much pressure on him. He'll be a big player for England, but it can't just be on one player's shoulders," Cole told Nuts magazine.
"In (Arsene) Wenger and (Fabio) Capello, he's working with two of the most experienced and respected managers in the world, who'll both help mature him as a player.
"Though, to be fair, scoring three goals against Croatia in the Maksimir stadium - probably the hardest stadium in Europe to go to - shows he's pretty fearless already.
"He's got great touch and fantastic ball control, which are obviously two of the essential skills needed on a football pitch, so he's definitely got the ability.
"What's so special about Theo is that by getting down the wing and picking out players, he's got the potential to set up as many goals as he'll score. Arsenal play great passing football, so he's learning his trade at a great place.
"He showed composure in front of goal against Croatia, like I said, you don't realise just how hard a stadium Maksimir is to play in, so he really did need a cool head on his shoulders."