That said, it is extremely hard to run as an independent and no one has ever been successful. Ross Perot came the closest in 1992, garnering about 19 percent of the popular vote.
Fagen believes Schultz may have a few things in his favor.
"It is difficult to get on the ballot based on the way our state laws are designed. However with somebody with that kind of brand power and name and wealth, it's certainly possible," she said on "Power Lunch."
What's more the number of people registering as independents is on the rise and has hit a 70-year high, noted Fagen, who is a CNBC contributor.
Schultz has taken a more active role in politics in recent years. However, in an exclusive interview with CNBC earlier Tuesday, he declined to specifically talk about whether he would challenge President Donald Trump in the 2020 election.
"There's a lot of things I can do as a private citizen other than run for the presidency of the United States," Schultz said. "Let's just see what happens."
However, he still opined on a number of political issues and revisited his criticism of Trump.
"I think the issues that we are facing in terms of the dysfunction and polarization that exists within the government is really based on a systematic problem of ideology and I think we need a very different view of how the government and how the country should be run," Schultz told CNBC.
He also took a few shots at Democrats, saying many leaders in the party were veering too far left.
Schultz served two stints as CEO of Starbucks and will step down as executive chairman on June 26. He'll then become chairman emeritus.