The Kiwis could play at one of the world's most iconic stadiums later this year at the Four Nations.
It is understood that tournament organisers are close to securing Anfield, the home of Liverpool Football Club, as the venue for the tournament final in mid-November.
It would be a considerable coup, as Anfield is regarded as one of the best football stadiums in Europe, alongside Old Trafford and the Nou Camp, and is famed for its atmosphere and history.
Liverpool FC has been based there - a few kilometres from the city centre - since 1892.
The ground has witnessed many famous European ties and also seen the English League Championship trophy paraded on 18 occasions.
Liverpool dominated English football during the 1970s and 1980s and while they have not won the league since 1990, the Reds remain one of football's best supported clubs.
Anfield also hosted games at the 1966 World Cup and 1996 European Championships.
League has been played at Anfield before. Widnes and Wigan played a Charity Shield match there in 1989 and the World Club Challenge between Wigan and Penrith was held there in 1992. Nearby club St Helens also played a couple of games at Anfield later in the 1990s.
The Kiwis look set to open the tournament against England in Huddersfield, before a clash with Australia the following week in Coventry.
After the success of the Kiwis vs England match at London's Olympic Stadium last year, it's possible England's match with Australia could be staged in the capital.
New Zealand's final group match against Scotland is set down for the unlikely venue of Workington.
If Anfield hosts the final, it would continue a pattern of famous English football grounds being used for showpiece league events.
The 2005 Tri Nations final - a memorable 24-0 win over Australia for Brian McClennan's Kiwis side - was staged at Elland Road, the home of three-time English champions Leeds United.
Wembley hosted a 2011 Four Nations match and the 2013 Rugby League World Cup final drew more than 70,000 fans to Manchester United's Old Trafford, although the match was forgettable for New Zealand league fans.