Joshua stopped Klitschko at Wembley in April to add the WBA world heavyweight title to his IBF crown.
Oct. 28 could be a potential date for the rematch, with the Principality Stadium being considered as the venue.
Wales’ rugby union team will play at the Principality Stadium for most Saturdays in November and December, leaving Oct. 28 free.
“Talks are ongoing over venues,” said Joshua’s promoter Eddie Hearn.
Joshua’s thrilling win over Ukrainian Klitschko was watched by a post-war record crowd of 90,000 at Wembley.
Staging a rematch outdoors could be difficult in the autumn, but the 74,500-capacity Principality Stadium’s retractable roof could make it a viable option.
Hearn has said he believes a rematch would go ahead in spite of its casting doubt over whether the 27-year-old Joshua could retain his IBF title.
The IBF has named Kubrat Pulev as a mandatory challenger, and says a fight with the Bulgarian must be next for Joshua.
As such, the IBF appears obliged to strip Joshua should he opt for a return fight with Klitschko, but Hearn has indicated he will put in a mandatory exception request.
Martyn Phillips, chief executive of both the Principality Stadium and Welsh Rugby Union, has previously said the governing body is discussing with various boxing promoters.
The stadium has already hosted speedway, rugby league, football and boxing, and Phillips says talks are continuing with the NFL.
If Joshua were to fight at the Principality Stadium, it would be the fourth time Wales’ national stadium has staged boxing.