David is the ex-wife of "Curb Your Enthusiasm" writer, producer and star Larry David.
Gore recently confirmed he and his wife Tipper had separated after four decades of marriage.
Star magazine said David and Gore, who worked together on the 2006 documentary "An Inconvenient Truth," have been linked romantically for two years.
"This is completely and totally untrue," David's representative told UsMagazine.com.
"It's a total fabrication. I adore both Al and Tipper," David told the Huffington Post. "I look at them both as family. And I have happily been in a serious relationship since my divorce."
2014: The Year in Music [PHOTOS]