That is according to the American’s promoter, who is waiting to hear back from the unified world heavyweight champion.
Joshua and his team have not rushed into any quick decisions over his next bout.
But the clock is now ticking, still there is no opponent in line for his date at Wembley Stadium on April 13.
It had been hoped that Joshua was set to take on the winner of the WBC showdown between Deontay Wilder and Tyson Fury.
It is now likely we will have to wait until later in the year to see the spectacle, after the Bronze Bomber and Gypsy King played out a controversial draw at the start of December in Los Angeles.
Wilder and Fury are expected to do it all over again so that there is a conclusive winner.
Dillian Whyte is the favourite to take on Joshua in April as he seeks revenge for the past.
AJ dispatched the Body Snatcher with a devastating seventh round knockout back in December 2015.
But Whyte has come back stronger since then having beaten Dereck Chisora twice as well as Joseph Parker, who is the only fighter to go the distance with Joshua.
Dmitry Salita who is one of Miller’s promoters, works alongside Matchroom’s Eddie Hearn and believes a fight across the pond could be Joshua’s break in the US market.
He told Sky Sports: “Jarrell [Miller] is the best American heavyweight, and has always expressed his interest to fight Joshua, so the ball is in his court.
“This is one of the biggest possible fights in boxing for 2019. If it happens at Madison Square Garden, it would bring back the heavyweight memories of Mike Tyson and Riddick Bowe, the boxing greats from Brooklyn, New York.
“Jarrell grew up in Brooklyn, it would be a huge event in New York.
“One of the biggest heavyweight fights in Madison Square Garden, literally and figuratively.”
Whyte, also promoted by Hearn believes time is running out over a fight with Joshua in April.
Speaking to iFL TV, the Brixton boxer said: “I don’t know what’s going on, I expected him and his team or Eddie Hearn to at least contact me.
“I’m not meeting Eddie until another two weeks or something, so I don’t know what’s going on.
“That’s not enough time to prepare for a fight like that. You need to know what’s going on so you start preparing from now.”