The 20-year-old singer, who had recently split from American model Kendall Jenner, was seen getting cosy with 35-year-old Mosshart at a nightclub during London Fashion Week, reported Contactmusic.
A source who spotted the duo said, "They were very touchy-feely in a booth and both pretty drunk. But they were having a great time together, laughing and joking with a lot of PDA.
"It was Harry who made the move as he was looking after her. At one point he was stroking her hair as she lay her head on the table. Harry's knack with women of any age is pretty amazing."
Styles was also linked to 32-years-old radio presenter Lucy Horobin, when he was 17 years, and more recently he apparently dated reality star Kendall, 18, for three months before they broke up in February due to work commitments.