President Donald Trump has fired back at former Starbucks CEO Howard Schultz after he announced he was mulling a 2020 US election bid as an independent.

“Howard Schultz doesn’t have the ‘guts’ to run for President! Watched him on @60Minutes last night and I agree with him that he is not the ‘smartest person.’ Besides, America already has that! I only hope that Starbucks is still paying me their rent in Trump Tower!” Mr Trump tweeted on Monday.

President Trump was legally required to divest from his businesses when he took office, so the “paying me rent” part of his tweet has also raised eyebrows.

In an interview on America’s 60 Minutes program on Sunday, Mr Schultz revealed he was “seriously thinking” about running for president in 2020 as a “centrist independent,” and challenged Mr Trump’s fitness for office.

According to Mr Schultz, 65, not only is Mr Trump “not qualified to be the president,” but Republicans and Democrats “are consistently not doing what’s necessary on behalf of the American people and are engaged, every single day, in revenge politics.”

Mr Schultz grew up in a working class neighbourhood in New York City, but made his fortune when he moved to the northwestern state of Washington in the 1980s and built Starbucks into a global coffee shop behemoth.

In June 2018 Mr Schultz stepped down as CEO of Starbucks amid whispers he was mulling presidential run.

There are legitimate fears among Democrats that if Mr Schultz runs against Mr Trump as an independent, he could make it easy for Mr Trump to get re-elected.

In 1992 conservative billionaire Ross Perot siphoned enough votes away from George H.W. Bush to hand the presidency to Democrat Bill Clinton.

And Democrats blame consumer advocate Ralph Nader for taking votes away from Democrat Al Gore in the 2000 election, allowing Republican George W. Bush to become president.

But during his 60 Minutes interview, Mr Schultz dodged a question about whether his potential independent run would make him a spoiler for the Democratic nominee.

“I wanna see the American people win,” he said. “I wanna 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’m not, in any way, in bed with a party.”

No third-party or independent candidate has won over 5 per cent of the popular vote since Ross Perot in 1996. But Schultz argued that a majority of the electorate is “exhausted” with politics.

“What we know, factually, is that over 40 per cent of the electorate is either a registered independent or currently affiliates themselves as an independent,” he said. “Their trust has been broken. And they are looking for a better choice.”