Drinkwater, 28, played a key role in helping Leicester City win the Premier League title under Ranieri's stewardship during the 2015-16 season.
The midfielder's form led to him joining Chelsea in a £35 million ($45m) move in 2017 but he has failed to make the grade at Stamford Bridge to date.
Drinkwater's time at Chelsea has been plagued by persistent injury problems, making just 22 appearances in all competitions under Antonio Conte last season.
Chelsea boss Maurizio Sarri revealed he "does not know" if Drinkwater has a future at the club in November, fuelling speculation over a potential departure in January.
And Fulham manager Ranieri was coy when asked about holding possible interest in reuniting with Drinkwater after his side's 2-0 defeat against Chelsea on Sunday.
Ranieri said after the match: "If I am interested I won't tell you [the media]. I'm sorry.
"In this moment, my mind is only on my team and how I can help my players improve and play together to be a strong squad. I have time to understand what we need.”
Should Drinkwater move to Fulham, one man standing in his way of a first-team berth is Arsenal loanee Calum Chambers.
Chambers has impressed in Ranieri's first two games in charge of Fulham, operating as a defensive midfielder as opposed to his usual centre-back role.
And Ranieri admits he has been "surprised" by Chambers' level of performance so far, adding: "He [Chambers] played very well [against Chelsea]. He's a good midfielder.
"He understands what I want and, also, when he has the ball, he moves it very quickly and in the right way. I'm very, very surprised."
Ranieri also had praise for his former Leicester charge and Chelsea star N'Golo Kante's display against Fulham.
Kante's recent performances had been criticised in the build up to the game, with many claiming the France ace is struggling in a more advanced role in Sarri's system.
However, Kante put in a strong performance for Chelsea, registering an assist for his side's opening goal through Pedro.
Ranieri said: "N'Golo is a fantastic player. Maurizio is right to pick on him sometimes. Not on only him but all the players, to improve.
"N'Golo played a very good match today.”
Next up for Fulham, who currently sit 20th in the table, is a league clash against Ranieri's former paymasters Leicester at Craven Cottage on Wednesday.
Chelsea, meanwhile, travel to Wolves in their next league outing on the same day.