Analysts forecast the report, to be issued by the Labor Department later in the day, will show an increase of about 165,000 jobs, which would leave the unemployment rate steady at 7.5 percent.
The figures' importance lies in how they are likely to affect the Fed's handling of its monetary stimulus program, which has been helping markets rally in recent months.
"I think market sentiment is still weak because there is still concern about what the next move of the Federal Reserve will be," said Linus Yip, strategist at First Shanghai Securities in Hong Kong.
Britain's FTSE 100 was flat in early trading at 6,340.02 while Germany's DAX was down 0.1 percent at 8,090.23. France's CAC-40 was 0.4 percent higher at 3,827.69.
European stocks stabilized after falling the previous day on disappointment with the European Central Bank after it failed to fulfill hopes that it would act to shore up economic activity in the region.
Wall Street was expected to open lower. Dow Jones industrial futures shed 0.2 percent to 15,010 while the broader S&P 500 futures lost 0.1 percent to 1,621.20.
The likely market reaction to the jobs report is difficult to predict. A tame jobs report could convince investors that the Fed's stimulus program will continue, which could support stocks. But if the figure is too weak, that could raise concerns about an unexpected economic downturn.
Fed Chairman Ben Bernanke has said the U.S. central bank might pull back on its $85 billion-a-month bond-buying program if economic data, especially hiring, improves significantly. Other Fed officials have spoken about a winding down of asset purchases sooner.
Earlier, in Asia, Japan's Nikkei 225 index lost 0.2 percent to close at 12,877.53 after the yen climbed against the dollar. That pummeled Japan's exporters, which generally welcome a weaker currency to make products more competitive overseas.
Japan's stock market has in recent months been beholden to the strength of the yen, which has become hugely volatile as investors estimated the likely impact of the country's aggressive new policy to get the economy growing again.
The yen on Friday strengthened against the dollar, which was 0.9 percent lower at 96.11 pounds. The euro was down 0.1 percent at $1.3235.
Elsewhere, Hong Kong's Hang Seng fell 1.2 percent to 21,571.01. South Korea's Kospi lost 1.8 percent to 1,923.85. Australia's S&P/ASX 200 shed 0.9 percent to 4,737.70.
In commodity markets, the benchmark oil contract for July delivery was up 34 cents to $95.10 per barrel in electronic trading on the New York Mercantile Exchange. The contract rose $1.02 on Thursday.
Pamela Sampson contributed from Bangkok.