Parker v Fa had been set to clash in Auckland on Saturday but a blood test from Fa ruled him out of stepping into the ring.
The postponement clearly frustrated Parker, who said he would have liked to have lined up another opponent.
“I’m still training, I’m in shape,” Parker said.
“I’m not sure what’s holding it up but hopefully everyone comes to terms to make it happen so the world can see a mega, mega fight.
Parker is already looking beyond the Fa fight, with an eye on Oleksandr Usyk.
Usyk is the WBO’s mandatory challenger and any potential bout against Parker would depend on Joshua vacating the WBO strap to secure a fight with Fury.
Joshua knocked out Pulev in the ninth round on Sunday but Parker was somewhat underwhelmed, backing Fury to emerge victorious if the two Britons finally meet in the ring.
“It’s a fight that we must see,” Parker said.