Minghella died March 18 of a hemorrhage after cancer surgery and Pollack died Monday of cancer.
The Hollywood Reporter said the filmmakers were partners in Mirage Enterprises and now that they are gone, the futures of the production company, as well as some of the projects Minghella and Pollack were working on, are unclear.
"We're all flying a little blind right now," a source close to Pollack's camp told the trade paper.
Insiders said Mirage projects not partnered with other producers might end up shepherded by Pollack's agents at CAA and his family.
The Hollywood Reporter said there is also speculation that Pollack's daughter Rebecca, who was an executive at United Artists, may take over Mirage.