Donald Trump has sought to goad Howard Schultz over his proposed 2020 presidential bid, suggesting the former Starbucks CEO “doesn't have the guts”.

The 65-year-old announced overnight he was “seriously considering” running for the White House as a “centrist independent”.

The president responded to the announcement, posting on social media: “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’. I only hope that Starbucks is still paying me their rent in Trump Tower!”

In an interview with CBS's 60 Minutes, the billionaire entrepreneur said he was mulling a bid for the presidency because he was tired of both parties engaging in daily “revenge politics”.

Mr Schultz's potential bid has already received criticism from both sides of the political aisle, with Democrats Julian Castro saying the move could “provide Donald Trump with his best hope of getting re-elected”.

Mr Schultz said in his interview on Sunday night that he wasn't worried about the president's backlash on social media.

“I think, like most people, I've become bored with President Trump and his tweets,” he said.