"And there will be developments that [Wall Street] will watch and see where they go," including trade, said Cashin, UBS director of floor operations at the New York Stock Exchange.
On Tuesday morning, President Donald Trump announced he plans to appoint CIA Director Mike Pompeo to replace Tillerson, the latest news in a string of personnel changes at the White House. Tillerson's departure at State followed a series of public disagreements with Trump.
Cashin said the market appears "intrigued" but satisfied with Trump's new choice for top U.S. diplomat. Additionally, the market feels "comfortable" with CNBC senior contributor Larry Kudlow as the possible choice for the role as top economic advisor, Cashin said.
On Monday, CNBC's Jim Cramer reported that Kudlow, a confidant of Trump and longtime economist, is the leading contender to replace Gary Cohn as the president's top economic advisor. And Trump said Tuesday that he is looking at Kudlow "very strongly" for the role.
"When Jim Cramer said that Larry might be the person on top of the list, it's not that [stocks] rallied so much, but certainly the selling stopped and we pared some of the losses," Cashin told "Squawk on the Street." "I think the market feels somewhat comfortable with that."
Stocks were higher Tuesday after the consumer price index for February showed U.S. inflation remains tame. Cashin called the numbers "very good," adding stocks should continue to rise from their recent lows.