Antonio Conte is believed to be in the market for a new target man this month.
Crouch, 36, only signed a new one-year deal with the Potters earlier this month and is being considered by the Premier League champions.
He has made 186 appearances for the Potters and netted 49 goals in all competitions, including five this season in league and cup.
Carroll has been ruled out for four to six weeks with an ankle injury.
Last summer, Conte failed to land Fernando Llorente, who moved to Tottenham Hotspur from Swansea City.