The couple, who got engaged last summer, were planning to tie the knot in June this year in California, reported Hello magazine.
"They were supposed to get married in June, but there have been so many problems with them, they thought it was best to work out their issues," a source said.
"They aren't ready. Their families are both concerned. They don't want to see Miley and Liam get married and then get divorced. They're very young to be getting married," it added.
Rumours about trouble between Cyrus and Hemsworth have been doing the rounds for a while now. But the couple have rubbished such reports.