According to Jacob Steinberg, the former Leicester City man will spurn the opportunity to move across town to the London Stadium, and will instead look to engineer a switch away from the Premier League.
It is unclear whether Drinkwater's exit is likely to be on a temporary or permanent basis, or whether the Blues will sanction the player to leave at all.
Certainly, the Blues now have a wealth of midfield options, with the likes of Cèsc Fabregas, Ruben Loftus-Cheek, Tiémoué Bakayoko and new loan signing Mateo Kovačić all vying with Drinkewater for a spot alongside N'Golo Kanté and Jorginho in the side's midfield three. With first team football looking unlikely, Drinkwater could well look for an exit before today's deadline.
The Hammers have had their most impressive transfer window in years, with new manager Manuel Pellegrini bringing in a host of new talent including tenacious wingers Felipe Luiz and Andriy Yarmolenko, as well as experienced goalkeeper Łukasz Fabiański. Drinkwater would be the icing on the cake for the club, but the chances of the deal going through appear to be slim.
The 32-year-old defensive midfielder has played in the Premier League before with Aston Villa, and will add further strength to the Hammers' squad ahead of the upcoming 2018/19 campaign.