The pair apparently face a telling off from producers over their backstage behaviour.
Jake and Kem have formed a budding bromance behind the scenes, but they're antics are reportedly going too far.
A show insider told the Daily Star newspaper: "Everyone likes a laugh and a joke but these two don’t seem to have an off button.
"Bosses are aware of their behaviour and they will be warned if it continues."
Jake himself insisted he and Kem were "serious" when they were on the ice.
"We take things seriously on the ice because we don’t want any injuries," he said.
However, he added: "But when the work is done we will continue to have as much fun as possible."
Jake and Kem are two of ten remaining celebrities on the current series, which continue Sunday night on ITV.
Meanwhile, the channel has confirmed that it has renewed Dancing On Ice for 2019.
The "greatest show on ice" will return to ITV next year for what will be its eleventh series overall.
The show originally ran on ITV between 2006 and 2014, before its revival this year.
Siobhan Greene, Head of Entertainment Commissioning, ITV, said “The show's welcome back has exceeded our expectations and it's been fantastic to see the audience at home loving it.
"The recommission is a no brainer and it's brilliant for everyone involved to know it'll be back next year.”
Katie Rawcliffe, ITV Studios Creative Director, added: “All of us missed Dancing on Ice while the show was off screen and it seems all our viewers did too… our on screen changes have been brilliantly received and we’re looking forward to getting our skates on for series two.”
The current series of Dancing On Ice airs on Sunday nights on ITV.