The Xtra Factor presenter apparently rejected the 24-year-old singer after they had grown close behind the scenes.
According to Star magazine, Arthur has described the TV host as "perfect" and is "smitten" with her.
Flack previously dated One Direction's Harry Styles after meeting him on the show, but is allegedly wary about dating another contestant.
The magazine report claims that Flack wants to remain "just friends" with Nicole Scherzinger's act.
The X Factor continues on Saturday at 8.20pm on ITV1.
Watch James Arthur's Halloween performance on The X Factor below: