The American, who blew Stiverne away in a devastating performance in just under three minutes, now wants to unify the belts against the Briton, who holds three versions of the championships.
In a video posted on his Instagram feed, Wilder tells Joshua not to delay the fight until 2019 or 2020 and to agree what would be a massive top division battle next year.
Wembley Stadium, Twickenham and Las Vegas have emerged as frontrunners to stage the contest, although Wilder faces competition from Joseph Parker and Tyson Fury in his bid to make the fight a reality.
