Rumors flew Thursday after Stewart posted a photo with the two-time Oscar winner at New American eatery Gjelina in Venice, California. In the image, the pair lean close over the table and smile brightly for the camera.
"Happy Birthday to this beautiful soul," wrote Stewart on the actress's 41st birthday.
However, PEOPLE has learned the photo is not recent – and the pair are simply longtime friends.
Stewart appeared on Desiree Hartsock's season of the long-running ABC reality show. The advertising executive was eliminated in week 9 of the show.
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The actress previously dated John Campisi, whom she split from after five years in 2012. Prior to dating Campisi, Swank was married to actor Chad Lowe from 1997 to 2006.