Ashley and Mary-Kate, who married Sarkozy, 47, in November 2014, have been vacationing in St. Ahead of the holidays, Ashley was spotted working out with Sachs, who owns a villa on the island.
The duo, who started dating this past October, also went for a romantic hike on New Year’s Eve and were photographed lovingly embracing each other while looking out over the ocean on a scenic cliff.
"They are dating," a source tells Us, but added that it isn't "that serious" just yet.
The couple's casual lunch outing, however, sparked engagement rumors.
The Full House alums previously went on a double date with their beaus in New York City on November 9, where Ashley was spotted kissing Sachs at a New York Knicks vs. After the game, the group headed to Sting’s 57th and 9th i Heart Radio album release party at Irving Plaza, where they continued to pack on the PDA with their partners.