Guardiola, who arrived at the Etihad in 2016, said Liverpool were the ideal opponents for his landmark game on Sunday as they had been his biggest rivals in England.
The Scots have never beaten New Zealand in 32 attempts over the past 120 years, with their best results two Murrayfield draws, 0-0 in 1964 and a 25-25 thriller in 1983.
Genge added: "I just made it clear to the boys that, although these people grow up on beaches throwing a rugby ball about and they're lovely people, they are very nasty to play against.
City and Liverpool have dominated English football over the past decade but this year both clubs are playing catch-up with Arsenal, who are six points clear of Pep Guardiola's second-placed team.