The Burlesque stars were not keen on seeing each other when they both turned up at a party hosted by CAA at Soho House in West Hollywood, where guests included Julia Roberts, Colin Firth and Demi Moore.
An onlooker said Aguilera, 30, was not happy to see Hough, 22, and a source said: 'Christina really got in her face.'
E! Online also claims Aguilera grabbed Hough and she then shouted: 'Don't touch me!'
Hough was said to be 'visibly upset' by what happened and a source said: 'The whole thing was troubling. People felt bad for Julianne.'
According to the US website, Aguilera's rep has described the report on the incident as 'nonsense'.