The 22-year-old, on loan from Manchester City, has been a hit for the Blues this season.
“It’s all there for him and it certainly looks as though he could be on the plane to the World Cup,” said McLeish.
“And if he makes a sufficient push and Capello plays him in the Egypt game and the rest of the warm-ups then he has an outside chance of playing in South Africa.
“It would be good to see Joe getting a crack because he has been excellent for us.
“He’s a superb keeper and he has improved no end since he came to the club.
“He’s a guy who works hard and has ironed out his rough edges.
“It’s not cut and dried though.
“The most experienced goalkeeper is David James and I’m sure Capello will stick with experience for the World Cup.
“But Joe can cope with all the scrutiny. I think he’s got the temperament for it.”