Meehan, who has a 42-5 record, and was considered unlucky to lose a WBO world title fight by split decision against Lamon Brewster in Las Vegas in 2004, would be at 1.96m the tallest fighter Parker has faced.
Meehan's last fight was a unanimous points victory over Kiwi Shane Cameron in Auckland last November, a win which effectively shut the door on Cameron's career. He was also the winner of the inaugural Super 8 tournament in Auckland last year with a knockout win over Michael Sprott in the final.
Parker's opponent for the fight at Waitakere's Trust Arena will be announced Tuesday.
Duco's Higgins has laid down a challenge for Parker's supporters in Auckland to respond in the way those in Invercargill - and before that Palmerston North for the victory over Yakup Saglam in June - have.
Both regions gave Parker a thunderous reception, with the 4,000-strong Stadium Southland crowd whipped into a frenzy for the main event following stunning knockout victories on the undercard by Izu Ugonoh over Will Quarry, and local hero Kaleni Taetuli against Dave 'The Brown Buttabean' Letele after 22 seconds.
The victory by Taetuli, a former Southland Stags loose forward, was as impressive as it was surprising - the previously undefeated Letele caught with a left hook from the opening bell and never recovering.
There was disquiet from some in the crowd about the manner of Parker's victory - some booed at what they thought was a dive by Tupou once they saw the replay - but there was no doubt Parker connected to Tupou's right temple with a left hand and followed it up with a heavy overhand right to the top of his opponent's head.
Parker said: "I felt it connected real well and when I looked down he was on the ground."
Trainer Kevin Barry was in no doubt about what he had seen and couldn't resist the opportunity to have a dig at critics who he said doubted Parker's power.
Barry said: "I still go back to two and a half years ago when the media and some people in New Zealand said Joseph Parker can't punch. I think everyone knows now that he hits as hard as any heavyweight in the world. I'm damn sure that fight being on ESPN and being seen by a lot of people around the world and with Joe's growing profile that we've sent some more shudders through the division."