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A fight against Dereck Chisora is all but set for October 26 in London, which gives Parker nine weeks to prepare.
However the process has been less than satisfactory for Parker's camp, which includes a recent offer they were forced to turn down.
The 26-2 Parker has had just one fight in 2019, a TKO of Australian Alex Leapai in Providence in June.
Chisora has a 31-9 record with victories over Senad Gashi and Artur Szpilka this year.
"It's nearly there," Parker said before flying to Las Vegas.
"The only frustrating thing for the last four or five weeks is that it's been very hard to communicate with them. Even though they are promoters, hard to get hold of. There was an email saying we will be on the card in London on October 26, still no contract or assurances. We want to head back into camp. We've been preparing well here and we want to prepare well back in Vegas but we're just waiting for the contract to be sent and signed," he added.
Parker's promoter David Higgins says it's been a bit shambolic.
"There's been a lot of talk for the past year or so about Chisora v Parker. That fight fell over last April because they ran the time down and left Joseph with only about seven weeks to prepare, so we called their bluff and pulled the pin. This time it's been similarly frustrating. It's now pretty tight but we've finally had something formal in writing and it was like extracting teeth…that's from our new promoter Eddie Hearn at Matchroom.
"He's a busy guy but if I was a conspiracy theorist I reckon it's old David Haye doing a little gentlemen's agreement with Hearn trying to delay us and leave us as little time as possible."