With Rooney now unavailable for England's group stage games thanks to his three-match suspension, Redknapp thinks Defoe could be the man to replace the Manchester United marksman in Fabio Capello's starting XI.
"It's up to Jermain to have a great season and push himself," said Redknapp, whose team faces Newcastle United on Sunday at St James' Park.
"It's wide open with England now. I think we will only play with one striker, with Gerrard behind somebody.
"You would take Jermain and Gerrard together all day long."