Wall Street believes a rate cut next month is a virtual certainty, with 38.5% odds on a 0.5% move and 61.5% odds on a 0.25% move, according to the CME FedWatch tracker.
"I'm leaning in the area ... that a July cut could be a 50-basis-point cut," said Cashin, UBS' director of floor operations at the New York Stock Exchange.
Central bankers voted last week to keep rates steady but indicated a cut was possible later in the year if factors such as the U.S.-China trade war were to really hurt the economy.
Fed Chairman Jerome Powell said at his post-June meeting news conference, "As always, we will act as appropriate to sustain the expansion, with a strong labor market and inflation near our" 2% objective.
The Fed generally likes to move rates in 0.25% increments, including the four hikes of that magnitude last year, bringing the fed funds overnight lending rate up to a target range of 2.25% to 2.5%.
The last time the Fed moved rates by more than 0.25% was in the dramatic cutting cycle of 2008, when central bankers were trying to boost the economy during the financial crisis.
At the end of 2008, the fed funds range stood at 0% to 0.25%, where it had stayed for seven years before incremental hikes started in December 2015.
On CNBC's "Squawk on the Street," Cashin said Monday that trade tensions between Washington and Beijing, which appear to be putting a drag on economic growth, are one of the main motivators for the Fed to cut rates.
Investors will be following President Donald Trump's meeting with Chinese President Xi Jinping at the G-20 summit in Japan later this week, where the two leaders are expected to reengage in trade talks under the threat of more levies.
Cashin said the markets would react to any positive comments on the trade front, but he admitted it's a "big leap" to get a trade deal because tensions have only been increasing lately.
Last week, Cashin warned the U.S. economy could be headed for a "borderline recession" by the fourth quarter if a trade deal were to remain elusive.