The Virgin boss has described the first time he met Trump at his apartment in Manhattan, New York.
Although it is not clear when the encounter took place, Sir Richard, 66, said Trump was discussing those who he had asked for help following his latest bankruptcy.
Sir Richard said Trump’s actions at the meeting were concerning as it showed Trump is “so wrapped up in himself” - a trait which is “dangerous if he got into the White House”.
The blog post reads: “Some years ago, Mr Trump invited me to lunch for a one-to-one meeting at his apartment in Manhattan.
“We had not met before and I accepted. Even before the starters arrived he began telling me about how he had asked a number of people for help after his latest bankruptcy and how five of them were unwilling to help.
“He told me he was going to spend the rest of his life destroying these five people.
“He didn’t speak about anything else and I found it very bizarre. I told him I didn’t think it was the best way of spending his life. I said it was going to eat him up, and do more damage to him than them.
“There must be more constructive ways to spend the rest of your life. (Hopefully my advice didn’t lead to him running for president).”
Sir Richard said he was left “baffled” at Trump’s lunch invitation.
The post continues: “I left the lunch feeling disturbed and saddened by what I’d heard. There are a lot of frightening things about this election; not least that policy has been pushed so far down the agenda.
“What concerns me most, based upon my personal experiences with Donald Trump, is his vindictive streak, which could be so dangerous if he got into the White House.
“For somebody who is running to be the leader of the free world to be so wrapped up in himself, rather than concerned with global issues, is very worrying.”
Sir Richard compared his meeting with Trump to one he had with his presidential rival, Democrat candidate Hillary Clinton.
In stark contrast to his encounter with the billionaire property mogul, his lunch with Clinton touched upon topics such as education reform, the war on drugs, women’s rights, conflicts around the globe and the death penalty, Sir Richard said.
He continued: “She was a good listener as well as an eloquent speaker. As she understands well, the President of the United States needs to understand and be engaged with wider world issues, rather than be consumed by petty personal quarrels.”
Sir Richard is the latest celebrity to speak out against the Republican presidential candidate as next month’s election draws closer.
JK Rowling, Robert De Niro and Frankie Boyle are just some of the big names to speak out against Trump.
In the third and final live TV debate featuring the presidential candidates, Trump suggested that he would reject the Presidential Election results if he was not named as winner.
He also interrupted Clinton when as she was answering a question, calling her a “nasty woman”. Earlier in the debate he claimed he “respects women” - to which the audience broke out in laughter.