Brook's promoter Eddie Hearn had been hoping to bring the fight to England but Alexander's team - he is promoted by Golden Boy - have insisted on a home bout for their man, with Las Vegas the likely venue.
Brook, who is unbeaten in 29 fights, became the mandatory challenger when he defeated Argentinian Hector Saldivia in Sheffield on 20 October.
Alexander, 25, will be making his first defence of the title after beating fellow American Randall Bailey on points in New York on the same night.
Hearn told ESPN.com: "We made a number of significant offers, well in excess of seven figures, to try and bring the fight to the UK, but Devon had no interest in traveling.
"We were at a 75-25 disadvantage in any potential purse bid and when we received the final offer from Golden Boy, we were all happy.
"If we won a purse bid and Devon vacated, we had all the potential to become a paper champion and that's not what Kell Brook is all about.
"To become great and make a statement, there is no better way than travel to a champion's country and rip the belt from him. Kell has the opportunity to make a huge statement in the 147-pound division."
Kevin Cunningham, Alexander's trainer and manager, said: "There's no reason to have to leave the country to fight a guy who no one in America has ever heard of.
"That was not going to happen. I'm just happy that I have a team and a promoter that was willing to step up and make this thing happen in the States and now we're just going to work to make sure this title stays in the States.
"Devon should be fighting someone with a bigger name than Kell Brook, but since he's the mandatory, we'll defend the title against the mandatory. But I don't see anything special about Kell Brook."