Jorginho is set to arrive at Stamford Bridge in a £50 million transfer from Napoli, in another knock to Drinkwater.
Drinkwater was tipped with a £30 million move to the London Stadium by the Telegraph earlier this summer.
However, there must be a question over whether West Ham actually need him now.
West Ham have already brought in Jack Wilshere this summer to strengthen their options in central midfield.
And Drinkwater would only arrive at West Ham facing a fight to earn a place in the team, much like he would at Chelsea now.
Indeed, it seems that the former Leicester man may well have missed his chance to join West Ham, and he may be relying on another club to offer him an escape route from Chelsea, with his first-team chances now looking very limited.