The 19-year-old singer has apparently tried to meet Lowe privately, reported Contactmusic.
"When Harry met Daisy there was a real spark. When they see each other they make sure it's in private at night or with a group of friends," a source said.
Lowe was previously dating 'Doctor Who' star Matt Smith.
Smith is said to be aware of the brewing romance between Styles and Lowe.
"Matt definitely knows about it because he mixes with a lot of the same people," the source added.