(CNN) Former Starbucks CEO Howard Schultz said on Sunday he is seriously considering running for president as a "centrist independent" in 2020.

"We're living at a most fragile time," Schultz told CBS's Scott Pelley in a "60 Minutes" interview that aired 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."

Last week, CNN reported two people familiar with Schultz's thinking said the businessman is exploring a potential 2020 presidential run as an independent.

A person close to Schultz's advisers said his team is "exploring a possible independent bid for the presidency in 2020," but the person emphasized that all options remained on the table.

"(Schultz) is thinking deeply about his future and how he can best serve the country," the person said.

Schultz, who describes himself as a "lifelong Democrat," stepped down as chairman and CEO of Starbucks last year, and said at the time he was exploring what he could do next to be most helpful to the future of America.

Democrats worried

If Schultz enters the 2020 race, he would join a growing list of candidates including California Sen. Kamala Harris, Hawaii Rep. Tulsi Gabbard, former Maryland Rep. John Delaney, and former secretary of Housing and Urban Development Julián Castro. Additionally, Sen. Elizabeth Warren of Massachusetts and Sen. Kirsten Gillibrand of New York have formed exploratory committees for a bid.

Several Democrats have voiced concern over a potential Schultz White House bid, including Castro on Sunday morning

Castro told CNN's Jake Tapper on "State of the Union," he is concerned that if Schultz runs "it would provide Donald Trump with his best hope of getting re-elected."

Castro said Trump's only hope at getting re-elected is if a third party candidate siphons off votes from the Democratic nominee. He said he doesn't think "that would be in the best interest of our county," and said, "I would suggest to Mr. Schultz to truly think about the negative impact that that might make."

"I have two words for Howard Schultz on a potential run for president as an independent: Just. Don't," said Washington State Democratic Party Chair Tina Podlodowski in a statement.

Podlodowski, the party chair in the state where Starbucks is headquartered and where Schultz once owned a professional sports team, also sent a fundraising email with the subject line "Howard Schultz could secure Trump's re-election," and added one more jab in a subsequent statement following the CBS interview.

"Howard Schultz running as an independent isn't about bringing people together," Podlodowski said. "It's about one person: Howard Schultz."

On Monday, New Hampshire Democratic Sen. Maggie Hassan also discouraged Schultz from launching a 2020 bid as an independent.

"I am very, very concerned about the impact of a potential spoiler here," Hassan told CNN's Poppy Harlow on "Newsroom." "Mr. Schultz is a life-long Democrat. I would encourage him to get into the Democratic primary and test his ideas that way."

When asked if he is worried about siphoning votes away from Democrats, Schultz told CBS, "I want to see the American people win. I want to see America win. I don't care if you're a Democrat, Independent, Libertarian, Republican. Bring me your ideas. And I will be an independent person who will embrace those ideas because I am not, in any way, in bed with a party."

Schultz said he sees "extremes" in both the Republican and Democratic political parties.

"Every American deserves the right to have access to quality health care. But what the Democrats are proposing is something that is as false as the wall. And that is free health care for all, which the country cannot afford," Schultz said.

Schultz also said he "100%" would release his tax returns. When Pelley pointed out Trump initially said the same but never did, Schultz said, "We can do it today."

'Injustice sparks a restlessness'

Schultz's new book, "From the Ground Up: A Journey to Reimagine the Promise of America," which is out on Monday, details his difficult childhood being raised in public housing in Brooklyn, New York. He describes the physical abuse he endured and says he was "haunted" by the financial insecurity of his childhood.

Schultz describes his parents hosting illegal poker games in their apartment and says he would hide in his room or in the stairwell of the building. He writes, "In me, injustice sparks a restlessness."

He describes his father as "closed off and unapproachable" -- explaining his father's inability to find good-paying work to support their family drove him to build a different kind of company. Schultz said he was "trying to build the kind of company that my father never got a chance to work for."

Schultz also details in the book his decades building Starbucks into the ubiquitous brand it is today and explains why, in 2011, he decided to speak out as CEO about controversial social issues including politics, race, and LGBTQ rights. He condemned the arrest of two black men at a Philadelphia Starbucks last spring and calls it a "blow to our soul."

For the first time publicly, Schultz waded into the controversy he faced as the owner of the former NBA Seattle SuperSonics -- a team he sold to an outside buyer, infuriating many Seattle residents. He owned the team from 2001 to 2006, and describes the move to sell the team to a group led by an out-of-state buyer as a "tremendous mistake," admitting in the book, "I had squandered the very public trust I had bought into."

In 2008, the franchise was moved to Oklahoma City, and its name changed to the Thunder.

Schultz writes it made him aware of the "negative ramifications attached to power" and writes "I will forever be deeply sorry."

Schultz created a Twitter account on Sunday and his first tweet reads , "It feels good to be here. My hope is to share my truth, listen to yours, build trust, and focus on things that can make us better."

Pelley said that after the CBS interview aired, Trump would likely tweet an attack on Schultz, to which Schultz responded: "I think, like most people, I've become bored with President Trump and his tweets."