The 29-year-old star has been seen getting close to Calum Best in recent days and eyebrows were raised after she was seen receiving a back massage from the reality TV favourite.
Jessica later admitted she had a bit of a crush on Calum, which Courtney learned from his TV screen at home.
The Apprentice runner-up warned that if anything happened between the pair, he would dump Jessica.
"If anything more was to happen then we won’t be dating anymore," he told The Sun. "At the moment we are just in the dating stages but when you’re seeing a girl and find out she’s kissing someone else then ‘Nah'.
Courtney Wood has threatened to dump Jessica Cunningham if she cheats on Celebrity Big Brother
Jessica and Courtney met while filming The Apprentice
Get me in the house
Courtney found himself subject to some online abuse after scenes of Calum and Jessica flirting aired.
At the time he hit back with a Tweet, which read: "Calum Best doesn't count, everyone loves Calum Best, even I fancy Calum Best."
The 29-year-old star has clarified that the comment was not meant as a defence for her behaviour.
Jessica has been seen getting flirty with Calum Best in the Borehamwood bungalow
Courtney has said he would like to go into the house and shake things up
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"People were calling her a slag and saying I had been mugged off. I got about 300-400 tweets, everyone was straight on it," he continued. "I wouldn’t say I jumped to her defence, I just gave my honest opinion on the situation. For me it wasn’t that hard or difficult."
Courtney is even considering entering the Borehamwood bungalow himself to surprise the flirtatious twosome.
"If it ramps up to anything more then get me in the house," he added "I feel like I could provide some entertaining television."
Celebrity Big Brother continues tomorrow night at 9pm on Channel 5.