Parker's manager, Sir Robert Jones, announced the fight with Tutaki this week.
Dean Lonergan, whose company Duco Events promotes Parker and Fight For Life, said Tutaki's contract had not been finalised.
He did not believe the charges against Tutaki would interfere with plans to pit him against Parker.
"As long as he can legally get in that ring he is going to fight," Lonergan said.
"We have spoken to him and his manager and as far as I know we have an agreement, but we haven't got a signature."
After starting as a charity event that pitted rugby players against league counterparts in a bid to raise money for youth suicide prevention, Fight For Life has become an increasingly commercial venture, and Lonergan has faced criticism over the publicity-grabbing tactics used to sell it.
Last year's event pitted surfer Paige Hareb against television presenter Hayley Holt.
This year's show will feature hulking Warriors league player Manu Vatuvei fighting champion Olympic rower Eric Murray.
Pitting Tutaki against devout Mormon Parker looks like another publicity stunt, something for which Lonergan made little apology.
"We are in the business of entertainment and if Tutaki brings notoriety that is a bonus," he said.
"Joseph is at the development stage of his career and we think it is a pretty good fight for him. Tutaki is a 42-fight veteran and first and foremost this a development fight for Joseph. It's a good fight to take. If there is a promotional bonus then that has to be a good thing too."
- additional reporting, Anna Leask
