Joshua added the WBO title to his WBA and IBF straps on Saturday with a points win over New Zealand’s Joseph Parker.
The Brit subsequently called out WBC champion Deontay Wilder, a challenge he accepted the next day.
However, Joshua’s promoter Eddie Hearn believes Wilder plans to fight Dominic Breazeale first before setting up a unification clash at the end of the year.
And Express Sport understands the Matchroom Boxing promoter would rather take Joshua to the US ahead of a bout against Wilder in order to help sell the huge clash in the States.
Both Miller and Bryant Jennings have been mentioned by Hearn previously, but now the former has come out directly issued a challenge, believing the 21-0 Joshua is underestimating the scene in America.
“I will welcome him to New York. We can make the fight happen,” Jarrell Miller told Sky Sports.
“He is definitely taking [American fighters] lightly because he had a good experience with Charles Martin.
“It’s hilarious. Who have I fought to earn a title shot? Who did AJ fight to earn a title shot? Hilarious.”
“Big Baby” Miller, just like Joshua, has an unbeaten 21-fight record, albeit with one draw early in his career after being docked two points for pushing in a four-round contest.
The 29-year-old also has 18 knockouts on his record and will take on Johann Duhaupas in Brooklyn on April 28 on a card headlined by Daniel Jacobs and promoted by Hearn.
Miller is expected to reiterate his challenge to Joshua if he comes through that test and has already attempted to goad the 28-year-old over his first ever decision win on Saturday.
“He’s not as powerful as he thinks,” Miller added.
“I did not enjoy [Joshua vs Parker]. I fell asleep and my boys woke me up. Then my boys fell asleep and I woke them up.
“I thought Parker won but UK fans will think differently. Parker threw more punches, was more active, had a better jab. Joshua was getting hit by terrible stuff.
“Parker wasn’t the most powerful but he was tagging [Joshua], and hurt him.”
