Trump and Harris debated each other for the first time on September 10. Trump has said there would not be another debate before the November 5 election. He rejected a past invitation from CNN for an October 23 debate, accepted by Harris.
Trump and Harris face each other in what polls show to be a tight race for the election.
In its statement, Fox said a second debate - proposed for either October 24 or 27. - "would present an opportunity for each candidate to make their closing arguments".
Last week, Harris' running mate and Minnesota Governor Tim Walz debated Trump's running mate and US Senator JD Vance.
"THERE WILL BE NO REMATCH," Trump said on his Truth Social platform.
"SO THERE IS NOTHING TO DEBATE."
Trump said it was very late in the process now to have a debate.
Trump and Harris debated each other for the first time on September 10. (AP PHOTO)
Trump faced then-Democratic presidential candidate and US President Joe Biden in a debate in late June.
Biden stepped aside as presidential candidate less than a month after the disastrous performance. Trump had built a lead against Biden following the debate but Harris took over as candidate after Biden bowed out and her entry has tightened the race, with some polls showing she has a narrow lead.
In their September 10 debate, Harris put Trump on the defensive with a stream of attacks on his fitness for office, his support of abortion restrictions and his myriad legal woes.
