Meyer believes the holders have only improved since lifting the trophy on home soil four years ago, a period in which they have won 47 of their 52 matches, losing just three times.
“I must say this – and I really mean it, it’s not just talk – but this is probably the best team that’s ever played the game,” he said.
“Just look at their record the last four years. Usually after the World Cup there’s a decline in performance. Steve [Hansen, New Zealand coach] was there for eight years as an assistant and most of the coaching staff has gone on but they just got better after the World Cup which just doesn’t happen in world rugby.
“We as a team know that this must be our best performance ever if we want to beat them because they are the best team that’s ever played the game.”
Meyer, who has named an unchanged side for the Twickenham showdown, has pledged to buy opposite number Hansen a consolatory crate of beer if the Springboks upset the odds.
“The winning coach always brings the beer now,” he added. “I said: ‘The first time we beat you I’ll bring you a case of beer.’ What I really respect about Steve is that after our win he took it like a man, and said ‘I’m waiting for that beer’. Hopefully I can give Steve a case of beers on Saturday.”