The stand-up comedian has agreed a deal to be a housemate in the upcoming series on Channel 5 in January, according to The Sun.
If the former Big Break presenter were to appear, it would reunite him with host Brian Dowling, whom he fell out with while both were contestants on Hell's Kitchen in 2007.
Davidson caused controversy by calling Dowling a "shirt-lifter" and a "poof" during the show.
"Jim often says what he thinks, even if his views are at odds with most people," said an insider.
"He got himself into a lot of trouble when he was on Hell's Kitchen with Brian, but hopefully he will be on better behaviour with him this time.
"It's true to say there is no love lost between the pair of them, but Brian is a professional and this is part of his job."
Davidson said in 2007 that he wanted to "rip [Dowling's] head off" following the fallout with the former Big Brother winner.
Justin Lee Collins, MC Ultra and Katie Price are among the names linked with Celebrity Big Brother, which launches on January 3.
Photo gallery - Rumoured Celebrity Big Brother housemates:
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