According to The Sun, the Gavin & Stacey star was spotted with the daughter of Duran Duran frontman Simon Le Bon at a fashion show.
"Mat showed up at the Forever 21 show earlier this week and a few people were wondering why," a source explained. "It became pretty clear very quickly when everyone saw him with Amber. They were giggling like a pair of school kids and flirting like mad.
"The funny thing was that she was in a towering pair of heels and he is not the biggest, so he was looking up at her the whole time. They nipped out for a cigarette together at one point and the fashion gang with cameras were advised not to take pictures."
Kings of Leon star Jared Followill has also been linked to Le Bon after they allegedly swapped numbers at a London club recently.
"But Mat has slipped in first. He has had a few girlfriends over the last couple of years and has also been cracking on with his acting career," the source added.