"Once again the story is made up, spread to other outlets and now denied," Clooney, 48, himself says in a statement released after the rumors swelled on the Internet.
The leading man added: "But don't let facts get in the way of a good story."
The couple, who were first seen together last summer, made their first public appearance together at September's Venice Film Festival.
Earlier this month, PEOPLE reported Canalis, 31, will appear in five episodes of the TNT drama Leverage when the series, starring Timothy Hutton, begins its third season this summer. She will play a mysterious woman simply known as "the Italian."