Wilder retained his WBC belt and his unbeaten record by stopping Luis Ortiz in the seventh round of their rematch on Saturday night, and immediately looked ahead to staging two stellar fights.
"Next, we have Tyson Fury in the rematch," Wilder said. "The schedule is set for February so we'll see.
"After that, I'm looking for a unification bout. I want one champion, one face, one name. He goes by the name of Deontay Wilder.
"I want a unification bout with the winner.
"The heavyweight division is too small to have so many belts lingering around. There should just be one champion. I'm the perfect man for that job."
Joshua plans to regain the IBF, WBA and WBO titles from Ruiz Jr in two weeks on December 7.
Before any undisputed title fight, Wilder aims to readdress his rivalry with Fury - they fought to a thrilling draw a year ago.
Wilder had struggled to keep pace with Ortiz for much of their rematch on Saturday night until the knockout moment.
But he reacted: "I was very confident in my ability and my skill. SHARE THIS NEWS USING ANY OF THE BUTTON BELOW PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇