The data is expected to show a 3 million increase in jobs and the unemployment rate falling to 12.5 per cent from 13.3 per cent.
However, the May figures may well be revised after delivering a major shock last month. The data showed a 2.5 million gain in jobs when economists had been expecting that 7.5 million jobs had been lost.
The kiwi is still trapped in the same trading range it's been in since early June but Philip Poppe, a director at Forex, said he senses "a bit of a change" in market sentiment.
"Our feeling is, if we're going to get another wave of US equities falling off and the kiwi going down, it's going to be in the next couple of weeks," Poppe said.
Otherwise, the kiwi is more likely to break higher.
The news on the spread of Covid-19 is certainly bleak: the US recorded more than 51,000 new infections on Wednesday after six consecutive days of more than 40,000 new cases.
But Poppe said this is unlikely to unsettle financial markets, simply because it comes as no surprise.
The states where the surges in cases are occurring are mostly those that went into lockdown late and opened early, long before they had complied with official guidelines.
"You need shock and surprise and panic to get big moves in the market, but at the moment we're all waiting for it," he said.
The US Federal Reserve chair Jerome Powell's comments earlier this week reinforced the message that the Fed "is going to be running extremely accommodative monetary policy settings for some time so, from that perspective, I don't think anything's changed."
The kiwi dollar was trading at 93.82 Australian cents from 93.47 cents at 5pm yesterday, at 51.98 British pence from 52.10 pence, at 57.64 euro cents from 57.42 cents, at 69.77 yen from 69.34 yen and at 4.5892 Chinese yuan from 4.5505 yuan.
The bid price on the two-year swap was unchanged at 0.2025 per cent, while the 10-year swap was at 0.7575 per cent from 0.7525 per cent yesterday.