The British stars sparked rumours of a relationship after they were photographed getting cosy together in the audience at the MTV Video Music Awards in New York City last month (Aug13).
Goulding was quick to play down the reports, tweeting, "I love that holding hands with my friends means we're an item. In that case I am in many relationships. Lover not a hater. What the f**k."
However, in an interview with Washington radio station Click 98.9, the Lego House hitmaker suggests he was indeed romantically involved with the Burn hitmaker.
When quizzed about Goulding, Sheeran explains, "Normal people don't hold hands if they're just friends. It was going on, and now it's not."
DJ Brad Nolan then pointed out that the Vmas were not long ago, to which Sheeran replied, "I know, I know... She's a really cool girl, she's very talented. She's had a number one single for three weeks in England now, so it's all going well. We just tour a lot."
The singer went on to insist he doesn't hold hands with other female friends, like his tour mate Taylor Swift: "I haven't even been pictured with that many women. I'm on tour with (Swift). There's never been a picture that's come out (with Swift) - if you can find a picture of me and Taylor holding hands or whatever... You won't be able to because it doesn't exist!"