The pair – who arrived in Mammoth, Calif., New Year’s Day and are staying at a house with a group of friends, PEOPLE confirms – was spotted hitting the slopes on Friday.
The Keeping Up with the Kardashians star, 18, and the One Direction singer, 19, were with pals, but Styles, who previously dated Taylor Swift, could be seen gazing at the aspiring model.
“Kendall snowboarded and Harry skied. They were very cute together. There was a lot of flirting and smiling going on,” a source tells PEOPLE. “Harry was a gentleman and even offered to carry Kendall’s snowboard to the ski lift.”
Harry “was trying to stay low-key and kept his ski goggles and hat on the whole time,” the source adds. “He didn’t remove his goggles until he got back to the car, after hours on the slopes.”
The teens also hung out after hitting the powder and posed for pics with a fan at a snowboard shop.
Jenner and Styles first sparked rumors that they were a couple when they were spotted sharing a meal in West Hollywood in November.
But when the former X Factor U.K. contestant was asked by CNN’s Piers Morgan if a relationship was in the works, Styles replied, “Dunno.”