Sheffield native Brook squared off with Khan within the ring after his speedy 39-second stoppage of Phil Lo Greco in Liverpool.
Khan made his return to boxing after virtually two years out of the ring and set his sights on an extended-awaited home duel.
Brook was working for broadcaster Sky Sports activities and was within the ring throughout Khan's publish-battle interview.
And Brook shouted "Amir, come on, Amir," in the direction of his rival and added: "All of the followers need the battle and I would like the struggle.
"When you go within the jungle and chase stars, however when he will get in there with me, I'll make him see stars.
"I'm not Lo Greco, I'm Kell Brook, 'The Particular One' and I will deal with him.
Brook added: "I do know he's received very quick arms. I've sparred with him. He's obtained the quickest palms I've been in with.
"Timing beats velocity, I'm a seasoned professional, I will land that bomb on him, that brownie. I'll destroy him."
Khan was introduced beneath Eddie Hearn's Matchroom Boxing promotions banner, which means the Brook battle is extra sensible than ever.
Hearn stated: "I really like the Brook-Khan struggle, we'll have to see.
"I might hate someday for these boys get previous, look again and kick themselves for not making that struggle.
"I consider the British public need to see Khan towards Brook, and we should always ship what the British public need.
"We have now to sit down, we now have to discover a deal, we now have to make positive they get nicely paid.
"They need to bash one another up on the finish of the day."