The 'Bleeding Love' hitmaker originally record the track, which was penned by Ryan Tedder, but she admits it wouldn't have ''worked'' for her and was much better suited to the 26-year-old singer.
Speaking to Popjustice, she said: ''Actually, I've recorded quite a few songs that other artists have done really well with.
''They should all, clearly, buy me Christmas presents. The thing is, if I had released 'Burn', I don't think it would have gone on to do as well as Ellie's version. It wouldn't have worked for me. It just wouldn't have.
''It was meant to be hers, I'm glad she did it, and I think she did it really well. I really like Ellie Goulding, I'm a big fan.''
Meanwhile, the 28-year-old singer recently said she doesn't measure her success by her record sales because she's happy with the decisions she's made in her career.
She said previously: ''The thing is I see a lot of fans saying, 'You should have released this. You should've done this.' But everything has been me doing what I want to do. Success, obviously, to most people is if you get a number one, that's your success. For me, it's my own journey and I've released the songs I've released because it's what I'm feeling at the time and what I want to do. ''