The fighter is keen for the all-British bout to come to fruition after years of speculation even though he feels the pair "are past their best".
Khan said: "What’s the fight that everyone wants to see? Everyone wants to see the Kell Brook fight. We’ve been talking about it for years and years.
"Look, me and Kell are probably past our best, I’ll be honest. But at the same time, we’re both around the same age. I think it’d be a good fight between us to see who is still No. 1 in Britain."
Khan tipped himself to win in six rounds and suggested that his rival was backing out of the fight.
He told talkSPORT: "I spoke to Kell’s family and Kell’s father wasn’t interested in it, he said, ‘No, we’re gonna look at other options.’ What other option is there for Kell Brook to make a good payday and fight someone with a big name like myself? Unless he fights someone with a world title or in America.
"So I’m scratching my head man, I’m thinking like, ‘What’s he going through?’ What’s going on with Kell Brook? How come he doesn’t want the fight? Let’s make it happen … The prediction for me and Kell Brook? I knock out Kell Brook in under six rounds."
Khan is keen for the contest to take place in the UK once the coronavirus pandemic subsides.
He said: "We’re both British fighters, let’s make it in the UK. Doing that in a football stadium here, that could be massive. So let’s hope things open up. Once things open up properly and we sort out the third or fourth wave, let me put a beating on Kell Brook."