Appearing on Watch What Happens Live with Andy Cohen Thursday, Paltrow, 49, participated in a game of "Plead the Fifth," where Cohen, 53, asks celebrities a series of burning questions and the guest can only skip one of them.
Cohen asked what Paltrow's reaction was to Close last year saying that her Best Actress Academy Award win for Shakespeare in Love didn't "make sense" to her.
"I just heard this from you, Andy! I never heard about this," Paltrow said with a laugh.
When the late-night host asked if she wanted to "plead the fifth" and skip the question, Paltrow said, "Well, I guess I have to because I don't know enough about it. So I plead the fifth."
In an interview with ABC News' Popcorn with Peter Travers last November, Close, 74, opened up about her movie Hillbilly Elegy, as well as her feelings about industry awards shows. Close said performances can't be compared to each other, using Paltrow's win as an example of a choice that didn't "make sense" to her.
"I honestly feel that to be nominated by your peers is about as good as it gets. And then, I've never understood how you could honestly compare performances, you know?" said Close at the time. "I remember the year Gwyneth Paltrow won over that incredible actress who was in Central Station and I thought, 'What?' It doesn't make sense."
Popcorn/youtube; courtesy everett collection Glenn Close; Gwyneth Paltrow in Shakespeare in Love (1998)
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"So I think who wins has a lot of things to do with how things have been, you know, whether it has traction or whatever. Publicity, how much money did they have to put it out in front of everybody's sight," she continued, adding, "I have to be philosophical about it, if I was upset about it...."
In March 1999, Paltrow, 26 years old at the time, won the category, which also included: Cate Blanchett for Elizabeth; Fernanda Montenegro for Central Station; Meryl Streep for One True Thing; and Emily Watson for Hilary and Jackie.
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On top of Paltrow's recognition, Shakespeare in Love also won six other Academy Awards, including Best Supporting Actress for Judi Dench and Best Picture.
Close has now been nominated for eight Oscars, dating back to her first film performance in 1982's The World According to Garp. Most recently, she was nominated for Best Supporting Actress for Hillbilly Elegy.
"I'm very proud of the times that my peers have felt that my performance was worthy of attention," Close (who's won three Tony Awards and three Emmy Awards) also told Travers.