Pompey had a £9m bid for the Liverpool striker turned down last month but are set to come back with a £10m bid. Portsmouth believe this is a fair price for a player with only 12 months left on his contract.
"Harry [Redknapp] has made it clear he wants Peter Crouch. He's the sort of quality we want to add. We're not giving up," said Pompey chief executive Peter Storey.