The picture soon went viral and fans began to speculate if Sheeran, 22, and Goulding, 26, were more than just friends, reported E! Online.
A furious Goulding took to micro-blogging site Twitter to clarify things.
"I love holding hands with my friends means we're an item? In that case I am in many relationships," she wrote.
A source also said that the two are not in a relationship.
Previously there were rumours suggesting that the 'Lights' hitmaker was spotted kissing One Direction boy bander Niall Horan.