The pair are said to have first noticed each other at Boot Camp and have grown closer since they both moved into the £6 million X Factor mansion in Hertfordshire earlier this month.
"Frankie and Amelia are an item. It is early days but they are enjoying one another's company a lot," a source told The People.
Lily is quoted as saying: "He's actually a really sweet boy. He loves it that people think he's a party animal but he's lovely. We're so close."
However, several of the other X Factor contestants are allegedly unhappy with the couple's ongoing relationship.
The source added: "They keep saying they are there to work not to fall over those two kissing one another's faces off."
The X Factor continues on ITV1 tonight at 8pm, when four acts will be sent home by the judges. Cee Lo Green and reigning champion Matt Cardle will also perform.
Watch Frankie Cocozza talk to Digital Spy about his reputation as a womaniser below: