The 29-year-old is reportedly the favourite for the job after Rita Ora allegedly turned the position down.
A source told the Daily Star: "X Factor producers have made initial enquiries to see if Carly is up for a role on the show."
Simon Cowell apparently wants the Call Me Maybe singer because she's internationally famous.
The insider added: "It is early doors and no offer has been made but Simon is keep to get someone fresh who is current and has international appeal."
It was recently claimed that Simon, 55, and Cheryl Fernandez-Versini, 31, are the only judges definitely returning.
Louis Walsh appeared to quit the show during an interview last month, and Spice Girl Mel, 39, has allegedly been axed.
Others in the frame for a spot on the panel include former judge Tulisa, 26, and 41-year-old Robbie Williams.
Would you like to see Carly as a judge on the show?