The Sandringham-based outfit has reached the final on eight occasions and lifted the trophy five times. Only one team left in the competition has a better Cup pedigree.
But Mayne is delighted with the draw, saying it is the perfect scenario for his squad.
"We were pretty happy with it," said Mayne. "It's a great challenge to take on a such a big club, and when you play the big guns it is very easy to motivate the squad. Central have a great record in the Cup and it is going to be very tough but we are excited about the game."
Central have been drawn at home and are the overwhelming favourites, especially as they can include the likes of Angel Berlanga and Emiliano Tade in their squad - players who have experienced a Fifa Club World Cup semi final with Auckland City.
But Central coach Jose Figueria is wary about the dangers that Waitemata present.
"It's a potential banana skin for us," said Figueria. "They are a well-organised and well-drilled team and [coach] Michael Mayne has had experience with New Zealand age group sides. Any game where you have a big team against the underdog there is always the potential for a surprise and we just have to make sure when don't get caught out."
Waitemata have players with National League experience throughout their team, and another who was on the roster at the Football Kingz and also called up twice to the All Whites squad. They also have Cup pedigree, with several players who have been all the way to the final before (with other clubs), while Waitemata reached the last 16 in 2015 before being knocked out by eventual semi-finalists Mangere United.
"We have some experienced players in our team and I'll be relying on them to guide our young players through this match," said Mayne. "We have to be realistic. Central have so many threats and they will be technically better than us and fitter because they train more often. We'll have to change our approach but I'm confident we can cause them some problems."
Figueria guided Central to the final in 2014, when they lost to Cashmere, while they dipped out in the quarter finals last year at the hands of Birkenhead.
"I don't feel extra pressure but obviously we know all about the Central's history in the Cup and there is always an expectation that we will do well."
In other matches this weekend Cashmere Technical, featuring former All White Ben Sigmund, face fellow Christchurch rivals Coastal Spirit while Central League title challengers Napier City Rovers and Miramar Rangers meet on Sunday.
Up north, Cup holders Eastern Suburbs face a testing trip to East Coast Bays while Waiheke United hope to continue their unlikely run when they travel to Te Atatu.
Local pride will go on the line down south as Queenstown Rovers host Gore Wanderers and Caversham welcome Dunedin Technical.
Saturday 25 June
Universities vs Richmond Athletic
East Coast Bays vs Eastern Suburbs
Forrest Hill-Milford United vs Mt Albert-Ponsonby
Caversham vs Dunedin Technical
Cashmere Technical vs Coastal Spirit
Central United vs Waitemata
Queenstown Rovers vs Gore Wanderers
Hibiscus Coast vs Waitakere City
Te Atatu vs Waiheke United
Palmerston North Marist vs Island Bay United
Manukau City vs Bay Olympic
North Wellington vs Upper Hutt City
Metro vs Three Kings United
Sunday 26 June
Napier City Rovers vs Miramar Rangers
Tawa vs Wairarapa United
Postponed:
Mangere United/Ngaruawahia United vs Birkenhead United
