The Xtra Factor host, who has been linked to the One Direction singer since November last year, visited his mum Anne and stepfather at their house in Cheshire last weekend.
Anne is said to have been impressed by Flack following a family dinner.
"Caroline and Harry are a full-on couple now. Things are getting serious pretty quickly and they're in love," a source told the Sunday Mirror.
"At first it was just a fling, but now they're looking at a future together. Caroline seemed to make a great impression with Harry's mum and it was mission accomplished."
It was previously reported that Flack would meet Styles's family over Christmas, although she is thought to have gone on holiday to India instead.