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.
The rumours intensified 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".
Kyle unexpectedly announced his split from Imogen, 28, on his radio show last Tuesday.
"A lot of people have been hitting us up on social media, a few phone calls, some media inquiries about my relationship status," he told listeners.
"We haven't been living with each other for quite a few months now. Unfortunately, it's just run its course."
On Friday, Imogen gave her side of the story in a lengthy video shared on her Instagram Stories.
The influencer and animal rights activist said they "still love each other" and added that the split was down to "family and health issues" and "not anything else", which could imply there was no other people involved.
She said she might get back with the multi-millionaire in the future: "It may not be the end, the end may not be nigh."
Naked except for a fur coat, Imogen said: "We have a lot to deal with separately ... It's probably been one of the hardest years of our lives, separately.
"I've got so much family stuff, and there's so much health stuff involved between us.
"We just kind of want to get each other, get ourselves into the best form of ourselves we can be, without kind of just p**ing in each other's pockets.
"We still love each other very much, we speak every day. We still see each other, we deal with things with each other."
"Everyone's like, 'Is there something else?' But not really," she added.
WATCH: Imogen Anthony opens up about her split from Kyle Sandilands