The Spurs boss admires the England striker, but is still not sure that the finances will allow him to bring the player from Portsmouth to White Hart Lane...
Pompey manager Paul Hart confirmed this week that he expected the England man to leave Fratton Park, and the player himself has been reported as favouring a move to Fulham.
A potential switch to Sunderland broke down last week, leaving the two London sides as the player's remaining suitors. However, Redknapp can seemingly see little economic sense in the move as it stands.
"Portsmouth are trying to sell Crouchy and Sunderland were interested. I think Fulham's interested," he told reporters at a press conference.
"I like Crouchy, but at the moment I've got four strikers here. Four good strikers, so it's not a priority for us."
Redknapp was then asked whether such a statement meant that he was planning to 'get rid' of current Tottenham front man Darren Bent so that Crouch could be brought in. He affirmed that that was not the case.
"I haven't got to get rid of anyone," he asserted. "It's not a case of getting rid of anybody. It's a just a case of we're not desperate at the moment for strikers.
"I was asked the question 'do I like him?' [Crouch]. I said I did. I just felt that at that type of money it's an awful lot of money for, no disrespect, a 28, 29-year-old.
"Basically it's an expensive deal because there's no return when you pay that type of money, and obviously his salary's high.
"So it's something that I don't know whether it's possible for us to do that deal."
As for whether he could then envisage beginning the new season next month without Crouch, Redknapp humorously responded, "Well he's not here now! So there's every chance we'll start without him.
"It's just an expensive deal. But he's a good player and I like him. Most teams would be pleased to have him in their team.
"But the whole package looks expensive to be fair, I think that's the problem."
Spurs midfielder Jermaine Jenas has also been linked with moves away from White Hart Lane in recent weeks, with Aston Villa mooted as possible destinations for the former Newcastle United midfielder.
"Never heard a thing from Aston Villa," Redknapp asserted. "I don't know where those stories keep coming from. No one's ever contacted us.
"I don't want to sell Jermaine Jenas. He came back strongly last season, he's a terrific player. We don't want to sell our best players.
"I don't know where the Villa thing's come from because Martin O'Neill [Villa manager] has never rung me, and I'm sure if he was interested he would."
Zack Wilson, Goal.com