Close won the 1994 Tony when she originated the role in the musical.
The actors are reuniting after The Beguiled in a new horror-thriller from A24 Productions.
The movie will be adapted by David Birke, who wrote Elle starring Isabelle Huppert.
Miyazaki's return could be to create a feature-length version of Boro.
A24, the distributor behind Moonlight, has acquired the new movie about life in an Orlando motel.
Lucy and Desi will focus on the actress' 20-year-long marriage to Desi Arnaz.
"Sometimes you have to be a high-flying bitch."