He also claimed it would be the unbeaten young boxer's "first big fight".
"You know, he has his opinion," Parker said in response. "I believe that every fight we've had is a big fight and every fight we've had is a fight where I've learned a lot of things in the ring, I learn about myself and it's sort of pushed me to know where I can go."
However, it is likely to be a big fight for Parker due to Meehan's advantages when it comes to height, reach and experience. But Parker said he was well prepared for the challenge, thanks to his sparring partner, Polish-born Nigerian Izu Ugonoh.
"[Ugonoh] helped us prepare for it pretty well," said trainer Kevin Barry. "He's got an 84inch reach and I think his punches come a little bit faster than Kali's."
The fight had come at the right time for Parker, who had returned to New Zealand in his best possible condition with no injuries or health issues, Barry said.
"Kali's a big, strong, very experienced guy and the respect we have for Kali is one of the reasons why we've prepared so well for this fight.
"We will get the best that Kali has to offer and that's what we expect and that's what we prepare for."
Despite the challenges Meehan presented, Barry said he was confident in Parker's ability.
"We have huge confidence in our camp. Confidence comes with preparation and we prepare very very well, each and every time we sign to fight anyone.
"This is payday for them, for all the hard work they do in camp, training three times a day for seven weeks."
While Parker joked that the biggest challenge on the night would be "picking what I have for dinner", he said the most important thing leading up the fight would be staying healthy, focused and well rested.
And despite everything that's been said, he's keen to make friends with his opponent - after the fight of course.
"My message would be, let's have a great fight, let's let the hands do the talking and let's be friends later."
