Lutz, 28, and 21-year-old Cyrus hinted of a brewing romance after they spent time in Miami post a trip to Bahamas last month, followed by their dance at the opening of Beacher's Madhouse in Las Vegas last week, reported E! online.
But the 'Twilight' star recently told reporters he was "happily single" and dodged them with his smile saying "stupid" when they asked if he was dating the young pop star.
"Miley likes him a lot, there are a lot of similarities between Kellan and Liam. He is her type," a source said.