Schultz is "young, healthy and has such passion," Sonnenfeld said Monday on "Closing Bell."
"Howard has never been a member of the business roundtable. He's not a standard part of corporate America. He's a maverick," he added. "But he's always engaged in social issues. He's not going to stop now. He's now going to be Prometheus unbound. He's going to go soaring on this."
Schultz, who is seen as the architect of the modern Starbucks, told Andrew Ross Sorkin on Monday he has been deeply concerned about the nation — the growing division at home and the U.S.' standing in the world.
"One of the things I want to do in my next chapter is to figure out if there is a role I can play in giving back," he told the paper. "I'm not exactly sure what that means yet."
When asked if he was considering a run for president, he said, "I intend to think about a range of options, and that could include public service. But I'm a long way from making any decisions about the future."
Sonnenfeld, a CNBC contributor, said if Schultz "doesn't engage in something big, there is an awkwardness."
That's because if something goes wrong with current Starbucks management, people will run back to Schultz "like he's a potential government in exile."
"When they go outside if they don't engage in something else they wind up inadvertently becoming a magnet for disaffection of different constituents," he added.
When Schultz steps down he will become the chairman emeritus of Starbucks. He served as the company's chief executive from 1987 to 2000, stepping down to focus on the company's global strategy. He returned to the head position in 2008 in an effort to revitalize the brand and stepped down, once again, in 2017.
— CNBC's Sarah Whitten contributed to this report.