* Evans says he is supportive of further adjustments if needed
* Kaplan says he too is "open-minded" on rate cuts
* Fed funds futures: traders see 90% change of October rate cut
* Mester pushes back on idea of lots of labor market slack
MADRID/THE WOODLANDS, Texas, Oct 3 (Reuters) - Fed policymakers said on Thursday they are open to the possibility of another rate cut as data indicated that a slowdown in U.S. manufacturing is beginning to spread to other parts of the world's biggest economy.
"We will go to our next meeting, have a discussion about what's appropriate, and I'm extremely open-minded to making an adjustment if that's what the appropriate policy is," Chicago Federal Reserve Bank President Charles Evans said in Madrid, a few hours before a report showed growth in the vast U.S. services sector may be stalling.
Dallas Fed President Robert Kaplan, speaking in a Houston suburb after that report, cautioned against reading too much into a single data point, but said he too has an "open mind" and is watching "extremely carefully" to see if weakness spreads to the consumer and labor market.
"If we wait for weakness in global growth and manufacturing and business investment to seep into other parts of the economy... I think we likely have waited too long," Kaplan said.
Though the Fed's two rate cuts so far this year have reduced the likelihood of a severe downturn, they have not eliminated it, Kaplan said.
And while he does not want to fuel excesses in borrowing and risk-taking, Kaplan said, "I would rather use adjusting the Fed funds rate if we need to when it matters, which I think is doing it sooner rather than later."
After the services report, contracts tied to the Fed's policy rate soared, as traders ramped up bets the Fed will follow rate cuts in July and September with further reductions at both its next meetings.
The Fed has cut rates twice this year as U.S. businesses were hit by rising trade tensions with China, political risk including Britain's potentially chaotic divorce from the European Union, and weakening economic growth in Germany and elsewhere.
U.S. consumer spending and jobs growth have so far remained strong, momentum that Fed Chair Jerome Powell and other central bankers have attributed at least in part to the Fed's pivot from a tightening stance as recently as 10 months ago.
But Fed policymakers have said they are on the lookout for any signs that the hit from trade uncertainty and a weakening global economy is no longer confined to the U.S. export and manufacturing sectors.
On Thursday, the Institute for Supply Management (ISM)'s non-manufacturing activity index flashed just such a warning signal, falling to 52.6 in September, the lowest reading since August 2016.
Separate data earlier in the week showed an index of U.S. factory activity contracting to its lowest level in more than a decade.
Rate futures traders now see a 90% chance of a quarter-of-percentage-point rate cut at the Fed's October 29-30 meeting, and a better-than-even chance of a fourth rate cut by year's end that would bring the central bank's target range to 1.25% to 1.5% and completely reverse all of last year's tightening.
U.S. stocks also rose on expectations of further Fed rate cuts.
A government report on September jobs growth, out early Friday, could be pivotal as Fed policymakers weigh whether trade uncertainties are reaching deeper into the U.S. economy.
Cleveland Fed President Loretta Mester, who was against the decision to cut rates in July, on Thursday pushed back against the idea that the labor market could strengthen much further than it is now. Unemployment in August registered at 3.7%, well below most economists' view of a sustainable level without pushing up on inflation. (Reporting by Jesús Aguado and Jose Elias Rodriguez in Madrid, Lindsay Dunsmuir in Washington, Jennifer Hiller in The Woodlands, Texas, with writing by Ann Saphir in San Francisco; Editing by Andrea Ricci and Sandra Maler)