Jackson will take on Punk on June 9 in the latter's second professional bout after he lost to Mickey Gall via first-round submission at UFC 203 in 2016.
Jackson told TMZ Sports: "I'm just going in here to beat him up a little bit and show him it's not for him."
When asked specifically if his intention is to end Punk's UFC career, Jackson said, "I mean, yeah, but that was the primary objective from the jump. But at the end of the day, I guess he's a cool dude, I ain't got no ill will against him. I'm not going in here to hurt him."
Jackson dismissed the idea that he has been lined up as Punk's opponent to give the wrestler a better chance of winning.
Jackson has also backed himself on Twitter to come out on top:
Aside from age, the 33-year-old may not hold a clear advantage over the 39-year-old Punk, though.
Jackson has also had just one UFC fight in his career, and like Punk, he lost in his debut against Gall, also via first-round submission.
What's more, he lasted just 45 seconds in the Octagon, around 90 seconds less than Punk. It may not be shaping up to be a particularly high-quality bout, but it could be a close contest between the pair.