The England international, who scored 19 goals in a previous spell at Fratton Park, found himself behind Fernando Torres in the Reds' pecking order last season and looks likely to leave the club this summer with Spurs and Manchester City also said to be interested.
Chief executive Peter Storrie revealed boss Harry Redknapp is still keen to land his top target.
He told The News: "Harry has made it clear he wants Peter Crouch. He's the sort of quality we want to add to the team.
"We have made a fair bid for him and that was turned down but we are still interested.
"It's now the case that we have made known our position and Liverpool have made know theirs - we will see what happens after that.
"This is not the end of it. As in normal transfer negotiations there is still more talking to be done. That's how it works.
"We are not going to be giving up. Harry sees him as an important player and we will try to bring him to Fratton Park.
"At the moment both myself and Harry are away so there is nothing happening, we will see what the situation is after this week.
"But nothing will be happening with Peter's future in the meantime, either. It's a quiet time for transfers.
"We are still interested, he's a quality player."