Cross told Variety that the BBC is "very interested" in a miniseries focused on the glamorous serial killer, who appeared in the first two series of the Idris Elba cop drama.
"The only real question would be how many [episodes] and how often we would do it - whether it would be a one-off miniseries or a returning miniseries," he explained.
"The truth is I absolutely adore Alice. I don't like to imagine my life without Alice in some way or other. It's something peculiar, but she's far more clever than me, far more witty than me, far more everything than me. I've got storylines going around in my head like trains."
Cross described the planned project as "a mix between The Talented Mr Ripley and The Last Seduction" and revealed that it will likely be set in Alice's "natural habitat" of America.
However, he confirmed that he does not currently have a plan for the character of John Luther (Elba) to appear in the Alice mini-series.
"I think the first one would probably be a Luther-free zone, because their stories have diverged to a large extent," he said. "But there would be nothing to suggest they couldn't come together again.
"The great thing is they can survive independently of each other. Each of those actors is so kind of secretly magnetic. [Idris is] able to pull that intense relationship out of many, many actors he's worked with, and I think Ruth as Alice would be able to do the same."
Back in March, Cross announced his plans to end Luther as a television show following the upcoming third series, in order to focus on a movie version.
"We've got lots and lots of movie interest, and Idris and I [are being] very careful about what kind of movie we choose to do," he has now revealed. "We've got all kinds of criteria of how and when we should do the movie, and we just need to pick our offer carefully. But I'd love to do it next year."
