Joshua climbed off the canvas to stun Klitschko with an 11th round knockout in front of 90,000 fans at Wembley back in April.
The Brit was obliged to take on mandatory challenger Kubrat Pulev in his next bout but the IBF have, at Matchroom Sports' request, granted an exception.
As a result any rematch must take place before December 2 with October looking likeliest with the winner then facing Bulgarian Pulev.
The Principality Stadium in Cardiff is considered the frontrunner to host the fight, should it take place in the UK, because of the retractable roof.
But, with the Wales rugby team in action at home for four consecutive weekends across November and December, promoter Eddie Hearn has ear-marked 28 October as the most viable date for a fight in the Welsh capital.
Speaking last month he said: “I believe Klitschko will go ahead with the rematch so we are looking at dates. The Principality Stadium is not really available in November because of rugby so 28 October is the option. Most of December is available but I don't really want to go that late.
“Josh has a bit of a sore shoulder, Klitschko has had a tough fight, his face was bashed up. You have got two more weeks in May, all of June and after that they will be thinking 'right let's get back in camp'.
“Even if you started back in camp in August, then you have September and October so end of October can work.”
Due to expected ticket demand for any rematch, it appears that Cardiff remains the only viable option should the fight be staged in the United Kingdom.
But Hearn is also exploring the option of staging the fight overseas, which would make the 28 October date more flexible.
He added: “For Cardiff that date is an option and also December but I don't really want to go into December so we are looking at the MGM in Las Vegas, China and Dubai as options too.”
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