Liverpool have slapped a £15million price tag on the England international, a fee which Portsmouth are refusing to pay.
Redknapp admits he is keen to bring the striker back for a second spell at Fratton Park, but will not pay over the odds in order to get his man.
Crouch is desperate to find regular first-team football, while Pompey are keen to boost their attacking options.
"I don't know if the avenue for Peter Crouch is shut or not," Redknapp told The News.
"If Liverpool are asking £15m for him it is certainly shut.
"I like Peter, but he belongs to Liverpool at the moment.
"If the price is right something could happen. If they wanted £10m it would certainly be more interesting. We do need another front man.
"At the moment we have David Nugent, Kanu and Jermain Defoe. We need another one up there, at least.
"You need to have at least four strikers. So I need another good one up there."
Redknapp confirmed that his search for new faces has been restricted to the domestic market so far, but refused to rule out the possibility of branching further afield in an attempt to find players of the required quality at a price the club can afford.
"We're looking around at a few things at the moment," he said.
"We are still making enquiries. They have mostly been at home in England, to be honest.
"We are seeing what is possible."