Carroll, an England worldwide cost West Ham £15 million in 2013 deal from Liverpool, having initially joined on loan, and he has scored 25 Premier Leaguegoals in 86 appearances despite a number of injury problems.
The 18-year-old forward has always been linked with a temporary move to the Stadium of Light in January to join up with Black Cats boss Chris Coleman, who gave him his global debut for Wales.
Red Star Belgrade's Richmond Boakye is another target that the club began scouting at the start of the season, and he trained in Antonio Conte's Juventus side as a youngster. The 36-year-old Crouch certainly fits that profile.
"We never said we were interested in him [Batshuayi]".
Meanwhile, Stoke have denied they have received an approach from Chelsea, per Sky Sports.
Victor Moses was the last player to swap Upton Park for Stamford Bridge after spending the 2015-16 season on loan at West Ham but there could soon be another player joining that list.
The 54-year-old said: "I went to watch Chelsea play Norwich in the FA Cup on Wednesday night and I knew that would increase the speculation about Carroll and Chelsea with Batshuayi coming to us". Many are asking why they are not considering ex-Chelsea man Daniel Sturridge who is available from Liverpool.
With links to players like Andy Carroll and Christian Benteke, the preference seems to be for a target man. We try not to talk about players at other clubs because I'm there to watch a game and wasn't necessarily there to watch anyone individually.
Many Blues fans will be wondering how they got this place.
Conte apparently feels that Carroll would be a good cheap option to have in his squad, with the added bonus that he would be eligible to play in the UEFA Champions League.