Howard Schultz, who stepped down as the firm's boss last year, says he is considering running as a centrist independent candidate in 2020.
In a series of tweets, he said the current two political parties in the US were "more divided than ever".
"Let's discuss how we can come together to create opportunities for more people," he posted.
During an interview with CBS' 60 Minutes programme, Mr Schultz said he had been a "lifelong Democrat" but criticised the current two-party dominated system.
"We're living at a most-fragile time 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," he said.
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