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.
Texas principal bans speaking Spanish, stirs controversy
Britney Spears on kissing Ryan Gosling, Justin Timberlake in the Mickey Mouse Club