Drinkwater's crowning glory came whilst he was part of Leicester's astonishing title winning side of 2016, where he was one half of a formidable midfield duo alongside N'Golo Kante - he rejoined his Foxes teammate at Chelsea for £35m a year later.
The Blues appear to be willing to let the midfielder go though, with new signing Jorginho pushing Drinkwater further down the Stamford Bridge midfield pecking order. The Hammers will need to fork out and pay for his wages though, which are believed to be £130,000 per week.
Drinkwater has found game time an issue ever since arriving in west London, making only 12 Premier League appearances for the club last season. A move to Pellegrini's West Ham could be beneficial for the England international, as he looks to revive his ailing international career.
It appears the Hammers may be waiting for Real Madrid star Luka Modric to join Serie A giants Inter in a surprise switch, which in turn would free up a slot for Inter midfielder Matias Vecino to move to Chelsea. The domino effect would then be complete, allowing Drinkwater to complete a move to the London Stadium.
Should he join Pellegrini, he'll follow a number of other arrivals to east London this summer, with high profile stars Jack Wilshere, Felipe Anderson and Andriy Yarmolenko all joining the former Premier League winning boss.