Kyle's rumoured falling out with his radio co-host Jackie 'O' Henderson is the "drama" they are thought to be referring to.
The radio hosts are said to have been at odds with each other over recent weeks, with Jackie calling out Kyle for his "difficult" behaviour.
"Kyle is all about Kyle, chucking tantrums and making unrealistic demands," the source told New Idea.
"He is difficult to work with and she finds it hard when he is rude to staff."
The reports were rubbished by Kyle on Monday, however, after her took to the airwaves on the Kyle and Jackie O Show, describing the reports as a "fantasy".
Kyle and Imogen announced they had bought their first home together last year - a farm in Robertson, NSW.
The couple are said to live a normal life, away from the lime light.
"Social media has a perception of showing you what you want to see. But for us there is a lot of sitting around doing f**king nothing," Imogen told News.com.au last year.
"We have quiet nights all the time… that's all we do is quiet nights, like sitting in front of Netflix where we have shows we watch constantly.
"But we have things being constant too. We have a farm, he's up at 4.30am, so it can be a bit crazy."