“Sunday brunch #modernfamily,” the 45-year-old Goop guru captioned the snap, in which both men were sitting together with big grins on their faces.
Although a rep for Paltrow has yet to comment on the supposed engagement, ET has reported that Falchuk popped the question a year ago.
While that’s a long time to keep a secret, it wouldn’t be the first time the couple has been private about their relationship. In fact, they dated for a year before going public at Robert Downey Jr.’s 50th birthday bash in April 2015.
A source close to the actress previously told PEOPLE that Paltrow was “crazy about Brad.” While the source went on to say that Paltrow is “cautious about marriage” and “very happy with how things are,” they added that it wasn’t “out of the question” for the couple to walk down the aisle in the future.
RELATED VIDEO: Gwyneth Paltrow Is Engaged to Producer Brad Falchuk: Reports
The actress first met the Glee co-creator when she guest-starred on the show back in 2010. The duo began dating after Paltrow split from the Coldplay frontman after 11 years of marriage. She shares two kids with the rocker — daughter Apple, 13, and son Moses, 11.
Falchuk, 46, has two children, Brody and Isabella, from his 10-year marriage to Suzanne Bukinik, which ended in a divorce filing in March 2013.