According to Celebrity Laundry, Banks has allegedly been dating the 24-year-old Givenchy model for over a month.
Evans was hired as a new judge for the upcoming season of Top Model, after Nigel Barker and Kelly Cutrone were both fired.
Banks and Evans have reportedly been spotted together in and around Los Angeles, including an alleged romantic trip to Newport Beach, California.
The 38-year-old former Sports Illustrated model has yet to acknowledge the rumours of a possible relationship between her and Evans.
Last month, she was linked to 'Take Care' rapper Drake after the pair were snapped on vacation together at Disneyland.