Rimes performed a tearful tribute at a concert last week to Whitney Houston, who Cowell considered for an "X Factor" gig before her death on February 11.
Plus, Rimes' personal life, marriage to Eddie Cibrian and weight issues -- while polarizing -- have also drawn plenty of headlines, which would spur press coverage of the show.
Sources say Rimes is interested in joining the Fox reality hit, with one source adding that she's met with "Factor" co-producer FremantleMedia North America about the gig and other opportunities.