Redknapp's arrival a fortnight ago has inspired three wins and a memorable draw against Arsenal - putting the likes of David Bentley, Jonathan Woodgate and Darren Bent back in the England frame.
"I wouldn't want to criticise Fabio Capello's team because he's done so well but hopefully they can push themselves and get themselves with a chance of playing," Redknapp said.
Tom Huddlestone made England's summer squad to face Trinidad and Tobago - and he had a hand in all three of Bent's goals against Dinamo Zagreb in the UEFA Cup this week, while also scoring a 30-yard volley himself.
"If we can get a couple in there it would be great," Redknapp added. "Bentley's playing well, there's Huddlestone, Woodgate's back in good form and is fit and looking like the defender we know he is."