Based on the novel of the same name which takes place at the height of the AIDS epidemic in 1987, the gay romance film showcased Elio and Oliver's summer love story to 1983, around the time HIV was discovered.
The 46-year-old filmmaker said the disease would be "a very relevant part" of the next installment.
"I think it's going to be a very relevant part of the story. I think Elio (Timothee Chalamet) will be a cinephile, and I'd like him to be in a movie theatre watching Paul Vecchiali's "Once More" (a 1988 film about a man who falls in love with a man after he leaves his wife, which was the first French movie to deal with AIDS). That could be the first scene (in the sequel).
The filmmaker said he hopes the movies develop as a decades-long "Before Sunrise"-like series.
"In my opinion, "Call Me..." can be the first chapter of the chronicles of the life of these people that we met in this movie, and if the first one is a story of coming-of-age and becoming a young man, maybe the next chapter will be, what is the position of the young man in the world, what does he want - and what is left a few years later of such an emotional punch that made him who he is?" he said.
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