The Blues can move five points clear in Group C with a win at Stadio Olimpico, where both of Roma's league defeats have come this term.
Kante has been sidelined for almost a month with a hamstring injury sustained on France duty, while Drinkwater only made his Premier League debut for the club as a late substitute in Saturday's 1-0 win at Bournemouth.
The duo will come under consideration against Eusebio Di Francesco's side, with the extent of Kante's involvement to be determined on matchday.
"We've recovered Drinkwater and Kante. When you're out with an injury it takes some time to recover full fitness, though. [Victor] Moses will need some more time," Conte said at his pre-match press conference.
"Kante has trained with us. He trained also before the game against Bournemouth. I think it's very important, in this moment, to speak with the player and then see his sensation.
"There are two big games before the international break, against Roma tomorrow and then Manchester United on Sunday.
"But I like to repeat that the most important thing is to go game by game. The most important game is tomorrow, against Roma."
Conte reiterated his confidence in the long-term future of Alvaro Morata, who on Monday stressed his satisfaction with life at the Blues having earlier voiced his desire to settle elsewhere.
"I think Alvaro is a good person and is enjoying his time in London, enjoying playing with Chelsea, a great team," Conte said.
"And I know very well where he's living now with his wife. It was the same building that I lived in last season. A lovely place, and not so far from the training ground.
"When you stay abroad to work, and above all you work with a lot of pressure, it's good to have your family with you. This season, for example, I solved this problem because my family stay with me and we're enjoying our time living in Cobham.
"We are enjoying London, enjoying this league. It's a fantastic experience for me, for Alvaro, for every single player who decides to have this fantastic experience in a really tough league."