Hart is the man in form after a steady season for Birmingham and looks set to play some part tonight against Egypt.
The 22-year-old only has one cap and 125-cap Shilton, 60, told the Daily Star: "It would be a brave decision (to hand him the top job) but that's what winning the World Cup is all about. Joe has come from nowhere and done well at Birmingham. But it's a big ask for him to start our first game against the USA because of his lack of experience.
"He's a young lad, he's impressed Capello and he's full of confidence because he's having a good spell, but he's only played half a game against Trinidad (in 2008). There are only a few games to go to the World Cup so it would be a brave decision to throw him in.
"He would be an inexperienced No 1. But if he can get in the three who go to the tournament, who knows? If David James was fit and playing well, it's really between him and West Ham's Rob Green.
"But he's got a problem at Portsmouth with the team struggling."