According to reports, this isn't the first time Kyle and Tegan have headed overseas together.
The pair previously spent time together in the U.S. in late September, during the aftermath of his controversial Virgin Mary joke.
Rumours intensified on Monday when an Australian magazine hit newsstands detailing Kyle's new "relationship" with Tegan.
An anonymous source told the magazine: "Kyle has fallen for his personal assistant, Tegan. Everyone in Kyle's inner circle, including Imogen, has known about the relationship for a while, and given that Kyle and Imogen haven't lived together for most of the past year, I'm surprised the news hasn't come out before this."
Another insider told the magazine: "It's become increasingly serious. Kyle endorsed Tegan's brother's wine company, Nueva Sangria, to help out the family in June, and when Kyle was with Tegan in LA in September, they were clearly a couple. It's no secret to anyone in the inner circle."
However, Kyle's manager Bruno Bouchet strenuously denied claims made by the magazine, telling Daily Mail: "It's utterly ridiculous."
Bruno, who would not confirm the sightings of Kyle in LA due to "security" reasons, confirmed that the KISS FM host "will continue to be on the air until the end of the radio ratings period in early December".
Meanwhile, another source told The Daily Telegraph the rumours are true: "Everyone knows [Kyle and Tegan] are together... For Kyle, it is all about her, he doesn't spend time with anyone else other than her. It is common knowledge in [his] inner circle."
A source claims the reason for their split was largely due to Kyle’s reluctance to make a commitment.
“Imogen has desperately wanted to get married and have kids for quite some time now but unfortunately Kyle wasn’t ready,” a source told New Idea.
“Kyle has issues from his past that he speaks about openly but keeps people at a distance, especially since his first marriage to Tamara [Jaber].”
The source further claims the couple didn’t spend much time together and effectively lived ‘separate lives’.
“They would usually do their own thing,” the insider claims.
“Kyle would always be out, and Imogen wouldn’t hear from him – and vice versa.”