They previously dated and their characters had one of the more ill-fated on-screen love stories, but that doesn't mean things aren't back on--and getting hot--for Game of Thrones co-stars Kit Harington and Rose Leslie.

Are Kit Harington & Rose Leslie Rekindling Their Romance?

The pair, who were spotted getting cozy in London last week before flying into LAX together, were also spotted out and about in L.A. on Saturday during a shopping trip--and they seemed incredibly close the entire time, holding hands while walking the streets. One photo even showed Leslie leaning over Harington's shoulder as the two stared at his phone together.

Neither has commented on the possibility that they've rekindled their romance (they previously dated but were reported to have broken up in 2013), but their co-star Emilia Clarke seemed to approve of their reunion as she walked the red carpet during the SAG Awards later that night, telling Entertainment Tonight's Nancy O'Dell that she was happy for the two.

Kit Harington Finally Discusses Jon Snow's Fate

"My goodness! You know, we like to spread the love on our show. It's a beautiful thing. She's one of my best friends, so it's good," Clarke said. "I mean, there are worst things than being caught kissing Jon Snow!"

Harington and Leslie's characters were romantically linked while on the show, though the romance came to an official end after Leslie's Ygritte was killed during the battle between the Wildlings and the Night's Watch at Castle Black.

The two aren't the only GoT co-stars who have sparked speculation and rumors they were dating over the years either. Harington was also once linked to Clarke, while Lena Headey (Cersei Lannister) and Pedro Pascal (Oberyn Martell) have sparked rumors in the past, as well as Dean-Charles Chapman (Tommen Baratheon) and Nell Tiger Free (Myrcella Baratheon).

Game of Thrones season 6 premiere April 24 on HBO.

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Game of Thrones, Hbo, Kit Harington, Rose leslie