‘It’s dubious that there’s going to be comprehensive tax reform,’ Roger Altman says

Don't count on the Trump administration getting comprehensive tax reform done, former U.S. Deputy Treasury Secretary Robert Altman told CNBC on Thursday.

"It's dubious that there's going to be comprehensive tax reform — emphasize reform … broad-based, 1986 Reagan-like reform, on the individual side and the corporate side," the founder and senior chairman of Evercore said in an interview with "Closing Bell."

President Donald Trump campaigned on the promise of slashing corporate taxes from 35 percent to 15 percent, as well as cutting individual income taxes and reducing the number of brackets. House Republicans have their own plan, which includes a cut in the corporate rate to 20 percent and a border adjustment tax.

On Thursday, Treasury Secretary Steven Mnuchin told "Squawk Box" he wants to see "very significant" tax reform passed by Congress' August recess.

"We've been working closely with the leadership in the House and the Senate and we're looking at a combined plan," Mnuchin said.

However, the Trump administration is already late to the game, Altman said.

For example, the tax cuts from President George W. Bush and President Ronald Reagan were already on the table at this point in those administrations, as was President Bill Clinton's economic plan, he pointed out.

"They are missing the window. Part of it is the priorities they set," said Altman, noting that the administration's first priority — Obamacare — is already struggling.

"Can they succeed, for example, in lowering the cooperate rate? I hope so. We need that. But broad-based reform of the type that it took two to three years to do in 1986, I really doubt it," he added.

— CNBC's Jacob Pramuk contributed to this report.