The Xtra Factor presenter is leaving the UK for a month-long holiday in India without 17-year-old Styles, according to Now.
A source alleges: "He was crying. He loves spending time with her - he's fallen for her really hard.
"He'd fancied her for months before they got together and now he's turned into a real romantic. She's his first big relationship."
The couple's romance has come under intense scrutiny from One Direction fans and celebrities such as Kerry Katona due to their age gap; 32-year-old Flack is 15 years Styles's senior.
Rumours were sparked in October when the pair were spotted kissing at a party.