Howard Schultz, who has an estimated net worth of $3.3bn, stepped down as head of the coffee giant last year and is believed to be exploring his options.
The 65-year-old had previously donated to Democratic campaigns, describing himself as a life-long supporter of the party, but has since criticised both the Democrats and the Repuublicans.
“We’re living at a most fragile time,” Mr Schultz told CBS’s 60 Minutes on Sunday.
“Not only the fact that this president is not qualified to be the president, but the fact that both parties are consistently not doing what’s necessary on behalf of the American people and are engaged every single day in revenge politics.”There are fears that his run could draw support from an eventual Democratic nominee and ultimately hand Donald Trump another four years in office.
Among those urging him not to run as an independent are David Axelrod, the former adviser to Barack Obama and Tina Podlodowski, the Democratic Party chairwoman in Washington state, where Mr Schultz has lived for decades.
“For somebody who is professing to be a lifelong Democrat, I think to be running as in independent in this particular cycle is not a wise thing to do,” Ms Podlodowski said.
She also called on Mr Schultz to either run as a Democrat or invest in the party infrastructure.
Mr Schultz has been mentioned as a potential candidate many times before and has done little to quell speculation about his presidential ambitions since he retired from Starbucks last June.
I love our country, and I am seriously considering running for president as a centrist independent.
— Howard Schultz (@HowardSchultz) January 28, 2019