As executive chairman, Schultz oversaw the opening of upscale Reserve stores and massive Roastery showrooms as part of its new Siren Retail initiative.
He became Starbucks' executive chairman previous year, handing the chief executive job to Kevin Johnson at a time when growth in Starbucks' dominant USA market was showing signs of cooling.
Last week, the company closed its USA stores for several hours for bias awareness training for its employees, one of the measures it promised after the men were arrested as they waited for an associate but hadn't bought anything.
Mr Schultz, who retired as chief executive past year, is to relinquish his seat on the board on 26 June.
Schultz, 64, says he is considering many possibilities.
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While he did not address the presidential speculation directly, Schultz did tell the Times: "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".
"I intend to think about a range of options, and that could include public service", he said, when asked if he was weighing a presidential run.
Starbucks, which styled itself as a "third place" for Americans to congregate along with work and home, also because synonymous with an urban style that bred imitators and changed the food business. "But I'm a long way from making any decisions about the future".
He also credited the company with "balancing profitability and social conscience, compassion and rigor, and love and responsibility".
Starbucks' board named Myron Ullman, who was previously chairman and CEO of struggling retailer J.C. Penney, as its new chair and Mellody Hobson vice chair effective upon Schultz's retirement. Shares of Starbucks have risen 21,000 percent since the company's initial public offering in 1992; an investor who had put in $10,000 then would have more than $2 million today.
The move followed the April 12 arrest of two black men in a Philadelphia Starbucks, which sparked outrage, protests and soul-searching about racial tensions that have been exacerbated under President Trump.