Manager Antonio Conte is understood to want to bolster his attacking options this month having been left unconvinced by Michy Batshuayi, who could be in line to leave the club before the end of the current window.
Chelsea attempted to sign Fernando Llorente last summer only to miss out to Tottenham Hotspur, but Conte has not given up on his search for a target man and reports have claimed that he is now considering an unlikely bid for Carroll.
The 28-year-old has been plagued by injuries since joining the Hammers from Liverpool in 2012, but scored twice in West Ham's win over West Bromwich Albion on Tuesday night.
Carroll has been spoken of as a potential contender for the England squad at this summer's World Cup should he stay fit, and Conte is reportedly willing to give him another shot at one of the league's top clubs following his relatively unsuccessful spell at Liverpool.
Carroll has not managed more than 15 Premier League starts in any of his last four seasons, though, and would only be regarded as a back-up to main striker Alvaro Morata at Stamford Bridge.