Drinkwater joined Chelsea from the Foxes last year, but he has since struggled to hold down a regular starting role at Stamford Bridge and finds himself behind the likes of Jorginho, N'Golo Kante, Ross Barkley, Cesc Fabregas and Ruben Loftus-Cheek under new manager Maurizio Sarri.
Leicester are understood to have made an enquiry regarding Drinkwater's availability during the summer transfer window, but no deal materialised.
However, The Express reports that Leicester could now revive their interest in re-signing the midfielder when the window reopens in January.
Drinkwater is thought to be open to the idea of leaving Chelsea if first-team football continues to elude him before January, although Southampton and West Ham United could rival Leicester for his services.
The 28-year-old made just 22 appearances for Chelsea across all competitions last season, while his only outing of the current campaign came in the Community Shield.