Art Cashin says the market could continue to run higher into the end of the year, but warns that any of three events could put the kibosh on the rally: a European slowdown, a geopolitical flare-up and a continued rise in interest rates.

"The 'Santa rally' traditionally start the week after Thanksgiving, so we'll get a good look at it," Cashin said on Tuesday's episode of "Futures Now."

"The only thing that could throw it off is if the European economies start to stutter. Because the S&P has benefited from the fact that it's not just the U.S.—it's filled with multinationals that have made money in Europe—and I think we're doing a little pause for reflection here, trying to figure out how much the European component will kick in."

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More broadly, Cashin said "there's always the risk" that the hazard of a market decline outweighs the reward of further gains. He adds that this could be particularly true if a geopolitical conflict rears its ugly head.

"What troubles me is that everything away from the United States is kind of marched off the stage," said Cashin, the director of floor operations for UBS. "We've had a lot of geopolitical worries over the past two years, and they seem to have disappeared. And if suddenly [a geopolitical conflict arises], whether it's in the Middle East or something pops up in the South China Sea, then I think we could see a little take-back."

However, the most pressing worry for this market veteran is a far more commonly discussed one.

(Read more: Markets will come 'unhinged' if this happens: BofA)

"The most immediate domestic concern is what will happen to interest rates," Cashin said. "They are temptingly looking at that area between 2.7 and 3 percent on the 10-year [Treasury yield], and that could send a lot of bidders off the field."

—By CNBC's Alex Rosenberg. Follow him on Twitter: @CNBCAlex.

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