The 26-year-old welterweight has endured a nightmare spell with injuries forcing two postponements of his fight with WBA champion Devon Alexander before Brook's foot problem caused a third cancellation.
Stablemate Lee Purdy has instead been handed a shot at Alexander, while salt was added to Brook's wounds when Khan fought in Special K's hometown of Sheffield last weekend.
Khan held on for a points win over Julio Diaz after being floored in the fourth round and Brook remains confident he could halt his British rival.
There is growing demand for a fight between the pair, who have been embroiled in a war of words, and Brook would agree to the clash without a belt on the line.
He told Ringside Toe 2 Toe podcast: "I heard he looked terrible. He got put down in the fourth round. He didn't look good in the fight against a blown-up lightweight, who's getting on a bit, so that will teach him to come to my city and think he can take it over.
"To be honest I want the Amir Khan fight for the fans. I'm getting his fans on me on Twitter and you know my fans want to see it.
"Everyone is saying when are you going to get it on with Amir Khan? I think we should put it to bed and get it on, and we'll see that I will take him out."
Brook has no hard feelings towards Purdy after he stepped in to face Alexander, but believes the Essex man will be outclassed.
He said: "All the best to Lee Purdy, what can I say? He's definitely got a puncher's chance against Devon, but I think he's a level above Purdy. He'll dominate the fight, Devon Alexander."
A persistent foot injury has sidelined Brook for a lengthy spell, but he hopes to start training in the near future ahead of his expected comeback fight in July.
"Yeah I'm feeling a lot better, my foot's not 100 per cent yet, but I'm looking at getting back into the boxing gym," he said.
"I haven't been in the gym now for four to six weeks. I've got itchy knuckles to get back in there and start hitting the bags again."