Napier have won the cup four times, the most recent in 2002, while Olympic were winners in 2009.
In their first round CL match, Napier City Rovers ran out convincing 4-1 winners.
Meanwhile, two-time defending champions Cashmere Technical of Christchurch host fellow Mainland Premier League side Coastal Spirit as their bid for three straight titles rolls on.
Cashmere, who have recorded 3-0 and 1-0 league wins over Coastal this year, sit atop the league standings with Coastal in fourth place.
Further south, 1999 champions Dunedin Technical host Mosgiel AFC in the Football South-based round of 16 clash.
In the Northern Region, 2014 runners-up, and five-time champions, Central United host Three Kings United while 2008 winners East Coast Bays AFC will visit Birkenhead United as the North Shore rivals tussle for a place in the quarter-finals.
Central took a 4-2 win over Three Kings to open the NRFL Premier League season in late March while East Coast Bays and Birkenhead took a point each from a 1-1 draw in May at Shepherd's Park.
Tauranga City's cup run will continue as the NRFL Division 1 side look to knock out Premier League opposition for the second successive round when they host Eastern Suburbs. The four northernmost ties are completed by the match-up of division one team Mangere United and division two side Papakura City.