Fox and Green, who have been dating since 2004, broke off a previous 2-year engagement in 2009.
UsMagazine.com said Green proposed to Fox again June 1 on a beach Hawaii, however, during the excitement the 2-carat diamond ring he offered the actress got lost in the sand.
"Security and maintenance staff spent a couple of hours looking for it," an insider told the magazine. "No one found it."
Green is best known for his work on TV's "Beverly Hills 90210" and "Terminator: The Sarah Connor Chronicles."
Fox starred in two "Transformers" blockbusters.