The former boxer ended his career in the sport last year but would consider putting on the gloves again to trade punches with the "full of himself" Paul.
Speaking on Heart Breakfast with Jamie Theakston and Amanda Holden, Khan said: "Jake Paul, he gets on my nerves a little bit.
"I think the way he conducts himself, the way he acts and he's just full of himself as well and he thinks he can fight, he's only been boxing for like a year, so yeah, I'd love to fight him."
The former world champion is even prepared to jump up in weight divisions to take down the YouTuber - who has won eight out of his nine bouts.
Khan said: "He's been very lucky though, he's a little bit heavier than me but I don't mind putting the pounds on just to beat him up."
Meanwhile, Khan recently praised Tyson Fury's Netflix series and said that the pair's wives "are the bosses" at home.
The former fighter - who has been married to Faryal Makhdoom for 10 years - told Capital XTRA: "The wives are the bosses. They tell us 'do this' and we have to do it. They tell you 'jump' you say, 'how many times'. I’m telling you.
"It don’t matter, you might be going into the ring and knocking men out and knocking these big giants out but when you are at home, they put you in your place and we see that in mine and in Tyson’s documentaries.
He added: "I think it’s nice to see as fighters, we are normal people. For sportsmen and women, I think boxing, when it comes to boxing, we are the most simplest people."
Heart Breakfast with Jamie and Amanda, weekdays from 6am - 10am, and on Global Player.