As investors focused on Greece's meeting with euro zone finance ministers, Art Cashin warned Wednesday that if deadlines keep getting imposed on that country it could weaken stocks.
"If they keep running from deadline to deadline, it could well destabilize the market," the director of floor operations for UBS at the New York Stock Exchange said in an interview with "Squawk on the Street."
Instead, he thinks a six-month extension could be an easier solution.
Greece's finance minister, Yanis Varoufakis, is meeting with eurogroup finance ministers in Brussels on Wednesday to discuss a solution to the country's bailout program, which is about to end. He's expected to unveil new reform proposals and is also projected to ask for a bridge program to cover Greece's government funding needs while a new debt pact is worked out.
According to reports, German Finance Minister Wolfgang Schaeuble said Tuesday that it is "over" if Greece refuses the final tranche of the current aid program.
"People feel we can't go from day to day like that," Cashin said. "They're afraid of, to overstate the case, the potential of a Lehman moment. It doesn't look like it could be big. Can they exit gracefully? All those things will take weeks and months to work out and that's why the extension seems to be the most logical choice."
Cashin also had his eye on oil prices Wednesday, noting that if crude fell below $47 again, it may begin to put pressure on equities.
He also reiterated his belief that the Federal Reserve won't hike interest rates until 2016, and said small-business performance will be the indicator. That's because small business is the backbone of the American economy, he said.
"If [Fed chair Jane Yellen] thinks still they're still risky but on the edge of improving I don't think she is going to raise rates."
—CNBC's Holly Ellyatt contributed to this report.