Khan continues his comeback to boxing on Saturday night when he fights Samuel Vargas in Birmingham.
The Bolton-born boxer returned to the ring in April but only took 39 seconds to knock out Phil Lo Greco.
A fight with fellow Brit Brook has been rumoured for later this year and Brook is keen to make it happen sooner rather than later.
“I’m going to the fight,” Brook told talkSPORT.
“I think we’re running out of time now, I think this is more or less his last chance to get it on with me.
“I’d love to take the fight at the end of this year.
“That’s what the world wants to see, Brook v Khan.
“I actually went in the ring for his last fight and he ran out of the ring when I got in.
“All I want to do is make this fight happen for all the fans.”
Khan has cooled speculation over a potential fight with Brook but Brook says he needs to stop with the excuses.
“He’s a little b**** to be honest with you, he is,” Brook added.
“He’s tried every excuse in the book to not make the fight.
“It’s gonna kill me to make 147lbs, but I’m willing to get down and make that fight.
“There’s nowhere else for him to hide in my opinion.
“What other excuses can he come out with?”