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.
Who next for Anthony Joshua?
Who next for Anthony Joshua?
1/6 Who next?
Joshua sensationally defeated Wladimir Klitschko - so who's next?
2/6 Deontay Wilder
A fight between Joshua and America's WBC heavyweight champion Wilder, 31, would likely prove the richest in the heavyweight division. The combination of two charismatic, explosive punchers would appeal both in the UK and the US, but may have such commercial potential that they would choose to delay until next summer. Wilder was ringside at Wembley, but has also been linked to fighting Tony Bellew.
3/6 Joseph Parker
New Zealand's WBO champion Parker carries less threat and appeal than Wilder but also represents less of a risk. The 25-year-old had been scheduled to fight Tyson Fury's cousin Hughie until injury ruled the challenger out, and is one of only two fighters against which a unification match-up could be made.
4/6 Wladimir Klitschko
The 41-year-old has already revealed he has a rematch clause he can take advantage of, and that only another showdown with Joshua is capable of convincing him to fight on. Joshua has also already said he would be willing to fight the Ukrainian again, but beyond financial gain there seems little benefit for the champion. Having already beaten him so entertainingly, Klitschko represents a high-risk, low-reward opponent.
5/6 Tyson Fury
Immediately after his defeat of Klitschko, Joshua called out the fighter who is quickly becoming his biggest rival. The 28-year-old Fury unsurprisingly responded on Twitter, writing "challenge accepted". Both seem confident of victory and willing to fight each other, both have beaten Klitschko and both represent the other's most intriguing opponent within the UK. Fury's biggest challenge could yet come in regaining his boxing licence amid his struggles with depression.
6/6 Tony Bellew
The former WBC cruiserweight champion's unexpected defeat of David Haye has given him far more appeal in the heavyweight division than any would have predicted. He seems incapable of providing Joshua with much of a test, but the money involved in fighting the champion will become such that any potential offers will be tempting. A match-up between the two is also straightforward to make, given they are both promoted by Matchroom. The biggest question may be whether Matchroom would rather use the 34-year-old Liverpudlian to further build Wilder's reputation before the American eventually fights Joshua.
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.”Reuse content