The President made the comments to a rally of his supporters in Macon, Georgia.
Mr Biden is currently the favourite to win when American’s go to the polls on November 3.
Addressing his supporters Mr Trump said: “You know what – running against the worst candidate in the history of presidential politics puts pressure on me.
“Could you imagine if I lose what am I going to do?
“I’m going to say I lost to the worst candidate in the history of politics.
“I’m not going to feel so good.
“Maybe I’ll have to leave the country, I don’t know.”
Mr Trump’s supporters laughed at the comments, which appeared to be made in jest.
However some of his opponents mocked the President on social media over the remarks.
The Lincoln Project, a group of anti-Trump American conservatives, retweeted the video with the caption “Promise?”
This received over 9,700 retweets and 78,900 likes.
In response Jim Madaffer, from San Diego, commented: “I’ll buy his one-way ticket!”
According to the latest Opinium/Guardian poll Mr Biden is currently leading the race by 17 points.
Ahead of Mr Trump’s arrival in Georgia he tweeted: “Getting ready to land in Macon, Georgia.
“Another giant crowd. See you soon!”