Wilder needed just 137 seconds to knock out Dominic Breazeale and retain his WBC heavyweight title on Saturday, improving his record to 41-0-1.
The American drew with Tyson Fury in December and there were calls for a rematch with the Brit or bout against WBA, IBF and WBO heavyweight champion Joshua.
Wilder – whose knockout of Breazeale was the 40th of his career – said a fight with Joshua would happen, but he remains unsure when.