City owner Thaksin Shinawatra told Sky Sports News today that Sven is interested in signing Crouch during the transfer window, as well as reinforcing the City midfield.
Crouch was a big favourite of Sven's during his time as England boss but Thaksin insists City will not break the bank for the Liverpool striker - or any other City targets for that matter!
"Sven is looking for one striker and one or two midfielders," he said.
"Sven does like Peter Crouch, very much. But he has yet to decide [whether to make an offer].
"We are looking for good players that are good money, not too expensive," added Thaksin.
"I am not in the position to buy everything at any cost. Sven will pick the right person at the right price."
However, Liverpool manager Benitez has poured cold water on City's interest, telling the Blues they will have to look elsewhere because Crouch is not for sale.
The England striker was thought to be eyeing a move after having limited first-team chances this season but Benitez has told Crouch he will get more game-time over the coming weeks.
The Spanish coach has also challenged Crouch to earn a new contract, with 18 months to run on his current deal.
"He does not play every game, but now with two games every week for some while he will get his chances to impress," said Benitez.
"I do not think it will be the situation that he will walk away for nothing in 18 months, that will not happen.
"The key is for him to score, play well and be happy. Then we will have the conversation about a contract.
"We do not want to sell Peter, we are really happy with him," he added. "Players in top sides know they cannot play in every game, but you can see how important he is for us.
"Against Porto in midweek (4-1 Champions League win), he and Harry Kewell were key substitutions that helped us win the game. We do not want to see any transfer movement involving him.
"In a top side you need good players, but they cannot play every game, that is impossible.
"Crouch is a key player for us, we do not want to sell him. But when someone is not playing every game other clubs ask about them.
"They will be trying to get close to the player. But we do not want to sell him, we want him here to help us win the title.
"Manchester City have done well this season, and they have some money to spend. But they will not have Peter Crouch."