The pair have apparently been causing all sorts of mischief behind the scenes.
Kem and Jake are said to have prompted to show producers to warn them they may be on, erm, thin ice.
“Everyone likes a laugh and a joke but these two don’t seem to have an off button,” a source told the Daily Star.
“Bosses are aware of their behaviour and they will be warned if it continues.”
Jake previously admitted to the publication: "We take things seriously on the ice because we don’t want any injuries.
"But when the work is done we will continue to have as much fun as possible."
Kem and Jake have formed a firm friendship on the show, much to the dismay of Kem’s Love Island BFF Chris Hughes.
He previously joked on Twitter that he had ‘blocked’ Jake on Twitter after seeing how close he’d grown to Kem.
GALLERY: Remember these Dancing On Ice winners?
CLOSER Dancing On Ice winners - slider with cover pic
1 of 12Think you can remember all the winners of Dancing On Ice? Let's see...
2 of 12Gaynor Faye, 2006
Emmerdale actress Gaynor Faye won the first ever series of Dancing On Ice alongside her professional ice skating partner Daniel Whiston, under the watchful eye of judges Robin Cousins, Karen Barber, Nicky Slater, Jason Gardiner and Karen Kresge.
3 of 12Kyran Bracken, 2007
Rugby player Kyran Bracken won the show - and the hearts of viewers - in the second series. Beating Clare Buckfield in the final showdown, Kyran won with his professional partner Melanie Lambert.
4 of 12Suzanne Shaw, 2008
Hear'Say singer Suzanne Shaw won the 2008 series with professional ice skater Matt Evers. Both of their final performances scored a perfect 30/30, which was the first time that had happened on the show, beating runner-up Chris Fountain.
5 of 12Ray Quinn, 2009
The X Factor star-turned-Broadway star Ray Quinn won the show in 2009 alongside his professional partner Maria Filippov. The couple beat out journalist Donal MacIntyre and his partner Florentine Houdinière with their final performance. He also won the returners' series in 2014.
6 of 12Hayley Tamaddon, 2010
7 of 12Sam Attwater, 2011
EastEnders' actor Sam Attwater won the coveted prize of first place in 2011 wth his partner Brianne Delcourt, beating TV presenter Laura Hamilton. The pair also returned for the 2014 series, but finished fourth.
8 of 12Matthew Wolfenden, 2012
Emmerdale actor Matthew Wolfenden won the 2012 series with his professional ice skating partner Nina Ulanova, beating fellow soap star Jorgie Porter to the top. This was also the year that Louie Spence joined the judging panel, if you remember...
9 of 12Beth Tweddle, 2013
Olympic champion gymnast Beth Tweddle won the 2013 series alongside her partner Daniel Whiston in his THIRD win on the show. She beat out EastEnders actor Matt Lapinskas and his partner Brianne Delcourt, and came third in the 2014 returners' series with Łukasz Różycki.
10 of 12Jake Quickenden, 2018
The X Factor and I'm A Celeb! runner-up Jake Quickenden finally won a reality show when he took part in Dancing On Ice in 2018 with his professional partner Vanessa Bauer, beating Coronation Street's Brooke Vincent - and she was NOT happy.
11 of 12James Jordan, 2019
James Jordan and Alexandra Schauman won 2019's trophy despite some fierce competition from Love Island's Wes Nelson and his partner, last year's winning professional Vanessa Bauer.Judges called their rendition of the famous Bolero "the best the show had ever seen" despite the first dance of the final failing to top the leader board. Early on in the 2019 competition, James was criticized for having an unfair advantage over the other contestants because of his extensive dancing experience.
12 of 12Joe Swash, 2020
Joe Swash and Alex Murphy took home the 2020 trophy, despite Diversity's Peri Kiely being the bookies favourite since the beginning of the competition.However, it wasn't all plain sailing for Joe throughout the competition. Not only did he find himself at the bottom of the leaderboard in week three and have an ear infection, he also had to swap professional dance partners after Alexandra Schauman fell and injured herself during rehearsals, forcing her to drop out of the show.
In other Dancing On Ice news, viewers were surprised to discover that Cheryl Baker's skating partner Dan Whiston has moved into her family home
The revelation came about on last night's episode of Dancing On Ice, after commentator Sam Matterface told the audience that Cheryl, 63, had moved 41-year-old Dan into her home.
But the Bucks Fizz star has been very open about the fact that her co-star is staying at her house in Kent with her husband Steve Stroud and their twin daughters Kyla and Natalie, 23.