The 34-year-old has been sidelined since November, as an investigation was launched over his failed test.
Joseph Parker returned an adverse finding in a Voluntary Anti-Doping Association (VADA) test after a cocaine-derived metabolite was detected in his system.
The test was conducted on the day Parker suffered an 11th-round stoppage defeat to Fabio Wardley.
Since the news emerged, he has strongly denied any wrongdoing.
In an interview with talkSPORT, he said: “It really rocked me.
“I think it’s funny, as a coach, it is probably your worst nightmare to find out that one of your fighters has failed a drug test, but the situation is quite strange.
“To test on the day of the fight, for a substance like cocaine, that is not performance enhancing, it’s probably the worst thing that you could do, going into a fight, is take cocaine.
“There has been an internal investigation as a team. His manager, David Higgins and I, and other people in the team.
“This is not for me to say right now, but it will come out. We are working with lawyers in the UK and appealing the decision.
“[Parker] doesn’t know how long he is banned for. He doesn’t really know what the ruling is yet, but there will be some appeal.
“Joe is quite confident that he will be exonerated with the evidence that I have seen and heard from Joe and David Higgins.”
Lee also confirmed that while the investigation is ongoing, Joseph Parker is not licensed to fight.
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