The Blues are looking to add to their attacking options this month as summer signing Alvaro Morata's five-game goal drought has contributed to Antonio Conte's men playing out three successive goalless draws with just two wins in their last seven games in all competitions.
With the Italian said to be concerned with not only Morata's form but Eden Hazard's as well, Chelsea were reportedly interested in the likes of Red Star Belgrade's Richmond Boakye and Crystal Palace's Christian Benteke.
However, recent interest in a loan move for Carroll is seen as the most attainable signing before the close of the January transfer window with Conte reportedly looking for a tall target-man forward.
And according to the Mirror, West Ham fear that interest from their London neighbours has turned Carroll's head as the 29-year-old is enticed by the prospect of playing in the Champions League.
The report also claims that out-of-favour Chelsea forward Michy Batshuayi has been offered in a swap deal for the Englishman, but the Hammers would prefer a cash-only deal.
Carroll returned from a knee injury in December and recently opened his league account for the season with a brace in West Ham's 2-1 win over West Bromwich Albion two weeks ago.
However, the former Newcastle United man is said to be nursing an ankle injury and having missed the club's last two games, is expected to miss West Ham's FA Cup third round replay against Shrewsbury on Tuesday (16 January).
Carroll joined the Irons on a permanent deal in 2013 after a forgettable two-year spell at Liverpool. Despite some injury problems, the Gateshead native has gone on to score 32 league goals in 110 games since his arrival.