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* Futures: Dow down 0.02%, S&P flat, Nasdaq up 0.10%

June 7 (Reuters) - U.S. stock index futures were little changed on Friday, as investors awaited a crucial employment report for confirmation that growing slackness in the U.S. labor market meant the Federal Reserve has more room to reduce interest rates.

The benchmark S&P 500 and the Nasdaq closed Thursday's session slightly lower, dragged by falling technology stocks despite touching intraday record highs in early trading.

Some megacap technology stocks that took a hit in the previous session were also slightly higher premarket, but overall trading was subdued ahead of the May nonfarm payrolls data, expected later in the day.

Economists polled by Reuters estimate that the U.S. economy added 185,000 new jobs in May, with the unemployment rate expected to hold steady at 3.9%.

Markets have struggled to anticipate the Fed's moves this year. Expectations for early rate reductions as soon as March dissipated quickly, as economic data indicated a tight labor market and persistent price pressures.

However, Thursday's weekly jobless claims report was the latest in a string of data suggesting the labor market is easing, potentially giving policymakers more confidence that they can ease rates while avoiding resurgent inflation.

"As always, the payrolls are a bit of a lottery, but the last few days of labour market numbers confirm that we are on an easing labour market trajectory," analysts at ING said in a note.

Traders now see a 68% chance of a September rate reduction, according to the CME's FedWatch tool, and have priced in about two cuts this year, according to data from LSEG..

Fresh inflation data is due next week, just before the Fed ends its two-day policy meeting on June 12. The central bank is expected to hold rates steady, but traders will await updated economic and policy forecasts for further clues on the timing and pace of future cuts.

Chipmaker Nvidia rose slightly in premarket trading, up 0.2% after losses in the previous session saw its market valuation slipping below the $3 trillion mark, behind that of Apple, again making it the world's third-most valuable company.

At 5:39 a.m. ET, Dow e-minis were down 6 points, or 0.02%, S&P 500 e-minis remained unchanged, and Nasdaq 100 e-minis were up 18.75 points, or 0.10%.

Among individual movers, GameStop's shares surged 33.2% premarket after stock influencer "Roaring Kitty" looked set to mark his return to YouTube. His channel on the platform showed an upcoming livestream scheduled for 12 p.m. ET on Friday.

Other so-called meme stocks rose, with AMC Entertainment and Koss Corp up 9.9% and 8.7%, respectively. Retail-focused trading platform Robinhood gained 2.9%

Lyft shares rose 1.7% after markets closed on Thursday, following a forecast of 15% annual growth in its gross bookings through 2027.

(Reporting by Lisa Mattackal in Bengaluru, Editing by Pooja Desai)