One insider said Hemsworth, 23, and Cyrus, 20 are "just weeks away from calling it off permanently."
"He is over her and wants to make a clean break," the insider said. "No more back and forth."
A second source said Hemsworth found Cyrus' raunchy performance at last month's MTV Video Music Awards show "mortifying."
The former "Hannah Montana" star was seen scantily clad, grinding against 36-year-old singer Robin Thicke and making vulgar gestures with a foam finger throughout her performance.
Hemsworth and Cyrus have been together for more than three years.