Eriksson has included Rooney in his World Cup squad despite the Manchester United striker getting injured last month and looking doubtful for at least the group stages in Germany.
"After May 25 we will know much better what is going to happen with Wayne Rooney...we have to wait and see how the scan goes," Eriksson told a news conference on Wednesday.
"I've always been positive but not because of medical reasons, I'm positive because I think he will do absolutely everything to try to get fit as soon as possible.
"Wayne Rooney not being in the World Cup -- I don't think even he believes that will be the truth. Of course he should be there."
Rooney is making progress in his recovery with United's medical staff and Eriksson believes the sheer drive of the 20-year-old will be an asset.
DESPERATE ROONEY
"I spoke to him last week and he's working, doing everything they are asking him, and maybe even more than that.
"Of course, he's desperate to play in the World Cup. He's one of the best players in the world... of course he wants to be on that stage."
Speaking at England's training camp in Portugal, Eriksson was reluctant to discuss his chosen option if Rooney is ruled out of the finals.
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Pressed over the Liverpool captain's role, Eriksson said: "I've known for many years that Steven Gerrard can play in a lot of positions and one is as a second striker.
"Of course, I hope we play with Wayne Rooney and Michael Owen up front - that's the best formation we have -- but Steven Gerrard is an option."
As for Cole, usually deployed in the problem position on England's left side, Eriksson added: "He can make life difficult for people if he plays on the left or as a second striker. It's a very good option."
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