West Ham and Leicester have been linked with moves to Drinkwater of late.
Chelsea are ready to sell the midfielder just 18 months after signing him from Leicester.
Drinkwater has failed to convince Maurizio Sarri of his worth in the first team and is expected to leave before January is out.
And bookmakers Ladbrokes have Fulham down as favourites to sign Drinkwater, which would see the England midfielder link up with his former boss Ranieri.
Ranieri and Drinkwater helped Leicester win their improbable Premier League title in 2016.
The manager was sacked the following season, while Drinkwater left for Chelsea in 2017.
Leicester are said to be open to re-signing their former midfield star but are 10/1 to get the job done.
And West Ham – who are in the market for new recruits this January – have drifted out to 12/1.
It appears as though Drinkwater will be heading to west London – rather than east – if he does remain in the capital this winter.
Alex Apati of Ladbrokes said: “Drinkwater’s hardly been value for money at Stamford Bridge but the odds suggest he could be about to make a much-needed move across London.”
As for West Ham, they are said to be interested in landing Jonjo Shelvey from Newcastle this month.
And a swap deal involving perpetually-injured striker Andy Carroll is said to be on the cards.
Carroll made his name at Newcastle before a move to Liverpool.
He has laboured for form and fitness ever since arriving at West Ham and manager Manuel Pellegrini could be set to ditch the England forward.