Higgins has received a letter from the WBO saying Parker, still undefeated after 23 professional fights following his success in his first title defence against Razvan Cojanu, must defend his title within 120 days.
Duco and Warren have 30 days to negotiate terms and if they can't it will go to purse bid again. Complicating matters is that Duco would much prefer Parker fought Tony Bellew in England in what would be a more lucrative bout before defending his title against Fury.
The Duco v Warren negotations, already off to a bad start, will probably not be straightforward, and Warren is likely to feel he holds an advantage following the revelations that Higgins and business partner Dean Lonergan are splitting, a divorce which is putting the future of Duco Events in doubt.
Warren will also be well aware that neither Duco nor Parker feel that fighting again in New Zealand in the short term is a viable option.
But Higgins denied any possible vulnerability to the Herald, saying: "We know what we're doing. It's just business as usual. I don't want to comment on any rumours, it's just about carrying on with the job at hand."
Higgins confirmed a fight against Fury in Manchester was a possibility, saying: "[We're] back to square one. If they give us terms that we think are reasonable we think it's not a bad fight. We think Joseph can go to England and win it. If they can't give straightforward terms we go to purse bid again. We won last time, we might win again this time."
Higgins added of the failed negotitations the first time around with Warren: "We went to them and asked 'what would it take for you to come to New Zealand?' And we couldn't get any sense out of them. They kept saying 'we will come, we won't come', it kept changing.
"Then they said 'we want to fight in England'. We said 'OK, here are the terms we need'. They couldn't even confirm what month the fight would be in or whether it would be the main event on the card."