(Reuters) - U.S. stock index futures were muted on Tuesday after the S&P and the Nasdaq notched record high levels in the last session, with focus on a crucial jobs report later this week along with more data and commentary from Federal Reserve officials.

October's job openings and labor turnover survey (JOLTS) report is due at 10:00 a.m. ET ahead of hotly anticipated monthly payrolls figures on Friday, a crucial metric in gauging the Fed's interest rate trajectory.

"The bumpy inflation trajectory since the end of the summer caught the Fed's attention and led markets to aggressively reprice the policy outlook for 2025," analysts at Societe Generale wrote in a morning note.

"It is unclear if we have reached an equilibrium with a terminal rate around 3.75%."

Traders currently see a more than 72% chance of the Fed cutting interest rates by 25-bps when it meets later this month, as per CME's FedWatch Tool.

Fed Governor Christopher Waller, whose views are often a bellwether for U.S. monetary policy, said on Monday that with inflation still forecast to fall to 2% he is inclined "at present" to support another interest rate cut later this month.

New York Fed President John Williams said late on Monday that while it was clear interest rates are likely go down over time, he could not yet say what the central bank's next move will be.

On the docket for Tuesday, comments from Chicago Fed President Austan Goolsbee and Fed Board Governor Adriana Kugler would be on the radar.

The Nasdaq and the S&P 500 scored to record closing highs in the last session, as the tech rally spilled into December after U.S. equities' stellar November performance.

Former U.S. President Donald Trump recaptured the White House in last month's election and his Republican Party swept both houses of Congress, boosting stocks in November.

Analysts have cited Trump's potential plans for tax cuts and deregulation as a positive for stocks, though tariffs would be negative on concerns of a global trade war.

At 5:08 a.m. ET, Dow E-minis were down 5 points, or 0.01%, S&P 500 E-minis were up 2.25 points, or 0.04% and Nasdaq 100 E-minis were down 3.25 points, or 0.02%.

Among early individual movers, Zscaler fell 7.6% in premarket trading after analysts noted that the cybersecurity firm's second-quarter revenue forecast failed to impress.

Tesla slipped 1.3% after the automaker's sales of China-made electric vehicles fell 4.3% year-on-year to 78,856 in November, data from the China Passenger Car Association showed.

U.S. Steel shed 6.8% after Trump reiterated his opposition to Nippon Steel's planned $15 billion the purchase of the company.