Miley, Liam split
There is also speculation that Liam was caught in a clinch with Mad Men star January Jones, while Miley was recently spotted without her engagement rings.
Liam is spending time in his native Australia at the moment and according to New York Post the pair are no longer in a relationship.
"Miley and Liam are done; it’s over. She likes to party really hard and can be pretty wild. It became a problem for him," an insider told the publication.
Another source added: "They have broken up before, and are broken up again now. There was drama because she suspected he had a wandering eye. And she recently tweeted a denial that he cheated.
"While Miley has insisted they are still together, right now they are very, very much apart."
Liam has been spending time with his brother Chris Hemsworth and his wife Elsa Pataky and daughter while in his home country.
Miley has been focusing on her music, something she promised to start doing on her Twitter page last week. After rumours about Liam and January reached fever pitch, she took to the social networking site to slam the speculation.
"I am so sick of La. And sick of the lies that come with it. I didn't call off my wedding. Taking a break from social media. #draining," she wrote.
"my new music is gonna shut everyone up. not discussing anything but my music from now on (sic)."
Although Liam is thought to be taking some time out from the relationship, Miley is reportedly determined to make things work.
"Miley is a fiery character, and they do fight, but she is crazy about Liam. She isn’t ready to accept it might be over for good," a source explained.
Neither of the couple's representatives has commented on the report.
Miley and Liam met while shooting movie The Last Song together in 2009. They had an on/off relationship during 2010, before working out their differences and getting engaged.
Last year, Miley insisted she wasn't too young to be engaged but wasn't planning to tie the knot any time soon.
"I don't really care about the wedding or the piece of paper as much as I do the promise we've made to each other. And we want to have a long engagement," she said.