Fury was denied one of the greatest comebacks in the history of the sport in December's drawn bout, one he appeared to have dominated.
Promoter Warren expects a deal to be done soon on an eagerly-anticipated rematch but talk of a move to Europe has been played down.
"We're trying to make that fight at the moment, everyone wants the fight and most importantly the fighters want it," he told ESPN.
"The venue is looking like the US, that's where the money is. Tyson was disappointed with the judging with the last fight, as I was, so a lot of things need to be sorted but the US is where they want it, probably in the second quarter.
"Vegas would be one of the options. I wouldn't want to go back to California, I didn't like working with the Californian commission and there were a lot of things we didn't like there.
"Tyson is already in the gym working hard, ticking over, and I think we would get it [the fight versus Wilder] before June."
There had been hope that Fury's long-awaited showdown with Anthony Joshua might happen early in 2019, particularly had Fury been given the verdict in Los Angeles.
However, Warren remains frustrated at Joshua's team, who he says do not want the fight.
"[Eddie Hearn] says all these things, but what he says and does are two different things. He [Eddie Hearn] said he wanted the fight for Joshua with Wilder last year when there was $80m on the table, but it didn't happen.
"Joshua will fight Dillian Whyte [at Wembley Stadium, London, on April 13], or Jarrell Miller next. We all know that.
"We're not complicated, Tyson is the most uncomplicated person you will meet, and he will fight anyone.
"He went to Germany to fight Wladimir Klitschko and he went to America to fight Wilder. It's Barry and Eddie Hearn's agenda that complicates it. Joshua is their cash cow and they want to keep milking it."
Related boxing links
