He now advises former New York mayor Michael Bloomberg, who is considering his own presidential campaign, as a Democrat.
"I think that would be a terrible legacy for anyone to leave," Wolfson said.
Washington State Democratic Party Chair Tina Podlodowski issued a statement Friday calling on Schultz to give up any consideration of an independent run.
"I have two words for Howard Schultz on a potential run for president as an independent: Just. Don't," she said in a statement. "Too much is at stake to make this about the ambitions of any one person."
Schultz, who has a net worth of about US$3.3 billion ($4.8b) and describes himself as a "lifelong Democrat," has not said publicly whether he will mount a presidential campaign and has kept open the option of running as a Democrat.
He will begin a national book tour January 28 for a memoir that describes his personal journey "to reimagine the promise of America."
Schultz's personal office did not respond Friday to a request for comment.
In all but two US elections, candidates have won the presidency by earning a majority of electoral-college votes.
But the entry of a credible independent candidate could scramble those calculations by denying anyone an outright victory.
If no candidate wins 270 or more votes, the victor would be decided by the House in a "contingent election," with each state delegation getting one ballot. The Senate would decide who becomes vice president. Such outcomes are historically rare, last occurring in 1824, when the House resolved a four-way race in favor of John Quincy Adams, even though Andrew Jackson had received the most votes.
Although Democrats make up a majority of the House, Republicans still have an advantage in the number of state delegations they control, with more Republican members than Democrats in 26 of the 50 states. Democrats are a majority of 22 House delegations. Two states, Pennsylvania and Michigan, have an equal number of Republican and Democratic members.
Calculations like this led Bloomberg, another billionaire, to decide against mounting an independent bid for the presidency in 2016. After an extensive research effort, he concluded that his candidacy could win enough electoral votes to push the decision to the House, but not enough to win a majority of the electoral college.
At the time, Republicans controlled a majority of seats in the House and the Senate. "The fact is, even if I were to receive the most popular votes and the most electoral votes, victory would be highly unlikely, because most members of Congress would vote for their party's nominee," Bloomberg declared in a 2016 article explaining his decision to stand down. He later endorsed Clinton.
Advisers to Kasich, a Republican critic of Trump, have been planning a 2020 run along parallel tracks, with separate blueprints for running as an independent and as a Republican in a primary challenge to Trump.
"I think for the first time, there is a legitimate chance for a third-party candidate," Kasich said in a November interview on ABC's "The View." "If you have the Republicans on the extreme and the Democrats on the extreme, there is a big wide-open space in the middle."
Kasich strategist John Weaver said the former Ohio governor will take into account the risk of inadvertently helping Trump's campaign before making a decision.
"Nobody would want to be a part of an effort that reelects Trump," Weaver said.
Upon his retirement last summer, Schultz said he would focus on public service, leaving open the option of a presidential run. "Let's just see what happens," he told CNBC in June.
He has spoken in his deliberations with a network of former Starbucks advisers and board members, including former New Jersey senator Bill Bradley, D, and Steve Schmidt, the former campaign manager for John McCain's 2008 presidential run.
He also has close ties, through the company board and his philanthropic efforts, with a number for former military officials, including former defense secretary Robert Gates and retired Adm. Mike Mullen.
As a CEO, Schultz cast himself as a compassionate leader who wanted to use his company for social good. He earned praise for the benefits he provided Starbucks retail workers, including a stock ownership plan, health-care coverage options for part-time employees and the opportunity to attend college free online.
When Trump announced a ban on US visitors from seven predominantly Muslim countries in January 2017, Schultz announced a company goal of hiring 10,000 refugees in stores around the world.
But he also has signaled a willingness to break with Democratic orthodoxy. "We have to go after entitlements," he said in the CNBC interview after announcing his retirement last year.
He also dismissed as "false promises" the proposals for single-payer health care and guaranteed federal jobs that have become popular on the left, arguing that they were fiscally unworkable.
At his March 2016 Starbucks shareholder meeting, Schultz opened his speech with a video montage highlighting the political divisions in the country, including still photographs of angry protests as well as the Democratic and Republican primary debates featuring Clinton and Trump.
The video ended with footage of Attorney General Robert F. Kennedy in 1968 calling for national unity and love in the wake of Martin Luther King Jr.'s assassination.
"We are facing a test not only of our character but of our morality as a people," Schultz told his investors. "The still photos in the video we shared are profoundly sad, and yet when we hear the heartfelt words of Robert Kennedy we are all comforted."
"We all long for that kind of leadership," he added.
