Joshua came out on top in last month's explosive heavyweight bout in front of 90,000 spectators at Wembley Stadium, maintaining his perfect record in the ring.
The WBA and IBF champion does not know who he will take on in his next outing, with Klitschko yet to decide whether to trigger his rematch clause, but promoter Eddie Hearn is hopeful that the fight will go ahead in the Welsh capital five months from now.
"I believe Klitschko will go ahead with the rematch so we are looking at dates," he told The Sun. "The Principality Stadium is not available in November because of rugby so October 28 is the option. Most of December is available but I don't really want to go that late."
Hearn revealed last week that Kubrat Pulev will be next in line to face Joshua should Klitschko retire from the sport.