Joe Biden would have become the oldest US President in history if he had beaten Trump
Mr Biden, who served under Barack Obama for both presidential terms, decided not to run after his son Beau died in 2015.
After Hillary Clinton’s shock defeat to Trump in the November election, questions have been raised about whether Mr Biden could have fared better against the Republican tycoon.
Do I regret not being president? Yes
Speaking to students at Colgate University in central New York, the 74-year-old was asked whether he had any regrets.
He responded: “The answer is that I had planned on running for president. And although it would have been a very difficult primary, I think I could have won.”
He announced his decision not to run in October 2015, just five months after his son Beau tragically died of brain cancer aged just 46.
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The White House Christmas Tree in the Blue Room of the White House in Washington, DC, November 29, 2016.
Mr Biden, a renowned popular member of Obama’s administration, said the “grieving process” would have made it too difficult to run for office.
He told the New York audience: "I didn't run because no man or woman should announce they're running for president of the United States unless they can look the public in the eye and promise you they can give you 100 percent.
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Obama and Biden were renowned for their close friendship
The pair celebrated after Obama won his second term in 2012
“At the end of the day, I just couldn’t do it. So I don’t regret not running.
“Do I regret not being president? Yes.”
In December, Mr Biden told reporters he is going to enter the race to become the US President in 2020 as the Democrat hopes to end Donald Trump’s presidency after just one term.
The former Delaware senator will be 77-years-old by the 2020 election, and some reporters were left wondering whether the grinning Vice President was serious about his intention to run.
He said: “Yeah, I am. I am going to run in 2020,” after he was asked if he would run for office again.
Joe Biden shares a joke with defeated Democrat Hillary Clinton
When asked if he was joking, he replied: “I'm not committing not to run. I'm not committing to anything.
“I learned a long time ago, fate has a strange way of intervening.”