She told Fox 5 News that Cook never promised to leave Brinkley.
The affair lasted about a year until she broke up with him in April, she told the Post.
According to the newspaper, Brinkley learned of the affair when she was approached by Bianchi's stepfather, a police officer, when she was speaking at a local high school graduation ceremony.
Bianchi has hired an attorney who says she is considering bringing a sexual harassment case against Cook.
Brinkley and Cook have a young daughter. Brinkley also has a son with ex-husband Richard Taubman, a real estate developer, and a daughter with Joel, whom she divorced in 1994. Brinkley's first marriage was to artist Jean-Francois Allaux.
Her publicist could not be immediately reached for comment.
With her clean-cut, all-American good looks, Brinkley's career as a supermodel spanned more than three decades. She has appeared on more than 500 magazine covers, in numerous television shows and been a spokeswoman for charitable and activist groups.