Promoter Eddie Hearn revealed earlier today that the two parties have begun talks over a potential all-British showdown.
The two fighters were involved in a heated exchange on boxing show Ringside, and Brook vowed to become the third man to knock Khan out.
"I'm very excited, we were on Ringside the other day, having a few words and I'm ready for that fight," he told Sky Sports News.
"Amir Khan has been knocked out at lightweight and light-welterweight, and I'll finish him off at welterweight, no problem.
"We need to get it on now, a big blockbuster for the fans in a big stadium. It's been talked about for a while now, so it needs to happen."
Brook must first get past Hector Saldivia when the two meet in a final eliminator for the IBF welterweight title next Saturday.