Joshua defeated 41-year-old Klitshcko after 11 rounds in British boxing's biggest bout to extend his winning streak to 19 fights. Klitschko's record now stands at 64 wins to five losses.
A clause in their contract allows the beaten fighter to ask for a rematch but Klitschko said he would take some time before making a decision.
"A rematch will be good, because of the type of fight we had," Joshua told reporters.
"I think he will want to fight again, because a fighter is the last one to know when to stop. But I think the team around him, his (soon to be) wife, because they normally wear the trousers, and his brother might advise him differently."
Joshua said he respected Klitschko and had no qualms about a rematch.
Read the full article on eurosport.co.uk: Joshua keen on Klitschko rematch after Wembley triumph