Klitschko says he will only take the December 10 fight in Manchester if the WBA belt is on the line too.
The WBA and WBO belts have been freed up by Tyson Fury who handed them over to concentrate on his battles with depression and drug use.
Joshua's manager Eddie Hearn said the next 48 hours would be vital as they seek a ruling from the WBA. In the meantime he confirmed he is looking at other options.
Hearn's easiest backup route is to call out Parker who is the mandatory challenger with the IBF.
Hearn had spoken positively about having Joshua fight Parker until the Klitschko option surfaced.
Parker's profile has only increased in the UK with all the fuss over the belts and his recent third round KO of Russian Alexander Dimitrenko which was broadcast there.
The complication for Parker is that with the Joshua having moved his focus to Klitschko, the Kiwi's handlers had also looked at a juicy alternative in the form of the vacant WBO belt.
They are angling for a WBO world title shot against Mexican Andy Ruiz in New Zealand.
That still has to be ratified as well, with the WBO expected to announce their plans for their heavyweight title at the annual convention in Puerto Rico this week. Dean Lonergan of Duco Events is attending that conference as well as Ruiz's handlers.
As Lonergan has maintained all along in this clouded process, Parker, with his No 1 positions in the IBF and WBO, is well positioned for a title shot either way.
Their preference, if they can pull it off, would still be to go down the WBO route because of the promotion being in New Zealand. Ruiz is also an easier prospect.
Win that belt, then your position strengthens as the process of unifying the four major titles ramps up.
Hearn is clearly growing frustrated at the time being taken by the relative organisations to decide what fights to sanction for their belts.
"The deal is there but we are awaiting sanctioning from the WBA," Hearn told Sky Sports.
"Both teams have written to the WBA to request sanctioning of our fight, but Wladimir wants the WBA belt to be on the line so until that is approved we cannot move forward.
"We expect news in the next few days, but in the meantime I believe both sides will look at alternative options for December 10 while we hope to get the news we need to make the fight happen."
Photo:Anthony Joshua's promoter Eddie Hearn still has plenty of work to do to tie down the next title fight for his IBF champion