Courtney Friel says she was speaking to the then-entrepreneur on the phone when he called her “the hottest” reporter on the channel.
“Out of nowhere, he said: ‘You should come up to my office sometime, so we can kiss’,” the 39-year-old writes in her new memoir.
“Donald,’ she says she replied. “I believe we’re both married.”
The revelation is made in her new book Tonight At 10: Kicking Booze and Breaking News.
She adds of the call: “This proposition made it difficult for me to report with a straight face on Trump running for president.
“It infuriated me that he would call all the women who shared stories of his bold advances liars. I totally believe them…
“At least now I can joke that I could have banged the president – but I passed.”
It is unclear when the advance is alleged to have occurred but Ms Friel worked at the New York based channel Fox as a correspondent and anchor for six years up to 2013.
After that she joined KTLA radio station in Los Angeles where she still works.
More than 20 women have separately accused Mr Trump of either unwanted sexual advances or sexual misconduct, dating from the early 1980s to 2016. He denies all of the claims.
The White House has said all the women are lying, while Mr Trump himself has suggested some were simply not attractive enough for him to sexually assault.
The White House has not commented on the latest claims from Ms Friel.