A spokesman for ABC News later apologised when the off-the-record comment was reported by Nightline co-host Terry Moran on his Twitter page.
According to audio obtained by celebrity gossip site TMZ, Obama said: "I thought that was really inappropriate. It was like, she's getting an award, what are you butting in?
"I hear you, I agree with you. The young lady seems like a perfectly nice person, she's getting her award, what's he doing up there? He's a jackass."
He added: "Now, now, all this stuff, I'm assuming all this stuff [is off-the-record]. Where's the [journalists'] pool? Come on guys, cut the president some slack, I've got a lot of other stuff on my plate."
West has since said sorry for the incident, while Swift has revealed that she accepted his "very sincere" apology.