Garner, 33, who plays secret agent Sidney Bristow on the TV series "Alias," and her 32-year-old boyfriend have been avoiding media scrutiny since they were first seen publicly courting in Boston last year, E! Online News reported.
Calls from the New York Daily News to the celebrities' spokesman and spokeswoman were unanswered Sunday.
Last month, Affleck threw a birthday bash for Garner at her Brentwood, Calif., home, and reportedly popped the question with a 4.5-carat diamond.
Garner's first marriage, to "Felicity" co-star Scott Foley, ended in divorce in 2004.