Swift claimed her former label, Big Machine Label Group, blocked her from playing her old hits at the American Music Awards. The star's master recordings fell into the hands of music manager Scooter Braun after he acquired Big Machine from Scott Borchetta for $300 million in June.
Rubenstein, whose Carlyle Group partially financed the sale of the record label, compared Swift's situation to an interview on a broadcast network.
"When you do interviews of me, you don't own the masters here," Rubenstein told Bartiromo. "It's owned by the company that you work for, and this is very true in many different businesses. It's true in the music business."
Swift made a fervent plea to Carlyle Group (and her legions of fans) to help her secure ownership of six multiplatinum albums she recorded under Big Machine, her former label.
"I'm especially asking for help from The Carlyle Group, who put up money for the sale of my music to these two men," Swift wrote in posts on her Instagram story, Facebook and Twitter.
Big Machine denied Swift's accusation.
Rubenstein remained hopeful that the parties would be able to reach an agreement.
"In that particular case, I do think there'll be a resolution of that in the near future," Rubenstein said. "Hopefully, [Swift] can continue to do very good music, but it's something that is more complicated than my being able to resolve it right here."
"In that particular case, I do think there'll be a resolution of that in the near future."
Ultimately, Swift played a mash-up of her old songs at the awards show.
"Taylor Swift is a great artist, and I enjoy her music," Rubenstein said. "I listen to it all the time, and I continue to hope that she'll perform great music."
FOX Business' Megan Henney and The Associated Press contributed to this report.