Drinkwater has been frustrated by a lack of game time at Stamford Bridge and will consider his future at the end of the season. West Ham feel he would "suit them perfectly," according to Matt Law at the Telegraph.
However, Chelsea would want to recoup as much of the £35 million they spent on the midfielder as possible, which could prove to be a major stumbling block for West Ham.
Drinkwater only arrived at Chelsea last summer from Leicester City but has failed to make much of an impact at Stamford Bridge. He's made just five Premier League starts and may be tempted by regular football elsewhere.
Chelsea manager Antonio Conte has said Drinkwater has been unlucky with injury this season, per ESPN FC's Liam Twomey:
England manager Gareth Southgate said Drinkwater's injury problems made him turn down offering an international call-up last November, per BBC Radio 5 live (h/t BBC Sport).
Goal's Nizaar Kinsella does not expect Drinkwater to feature at the 2018 FIFA World Cup:
Although he is only in his first season at Chelsea, it's understandable Drinkwater may be considering a move to revive a career that appears to have stalled.
Drinkwater proved his quality as part of Leicester City's Premier League title-winning side of 2015/16, forming a superb midfield partnership with N'Golo Kante.
Former goalkeeper David Preece highlighted some of his qualities:
The midfielder would expect to go straight into the West Ham team, although the Hammers would need to retain their Premier League status to have any chance of a successful transfer. David Moyes' side have flirted with relegation but are now six points clear of the relegation zone with six games left to play.
Drinkwater's future may also be affected by events at Stamford Bridge, with Conte's position at the club far from secure. The Italian could leave at the end of the season, and the Blues have approached Napoli boss Maurizio Sarri about replacing him, per Darren Lewis at the Mirror.
A new manager could mean a fresh start for Drinkwater at Chelsea, although the club's poor defence of their title and failure to impress in the UEFA Champions League may mean plenty of summer transfer activity.