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8 year oldAfter launching his candidacy as an outsider last year, Mr Trump went on to overcome all rivals to clinch the Republican presidential nomination.
Some polls have since indicated he is leading Democrat candidate Hillary Clinton in the presidential race.
Asked by NBC News if Mr Trump could win, Mr Obama said: "I've seen all kinds of crazy stuff happen."
"I think anybody who goes into campaigns not running scared can end up losing," he added.
Poll monitors had given Mrs Clinton a double-digit lead over Mr Trump for much of the presidential race, but that lead has since been whittled down.
Mr Trump received a boost nationally, and in key battleground states, after the end of his party's convention last week. Some polls now show he is in the lead over Mrs Clinton.
The Democrats' convention in Philadelphia ends on Thursday.
President Obama, Vice-President Joe Biden and Mrs Clinton's vice-presidential pick, Tim Kaine, will speak at the convention on Wednesday.
On Tuesday, Bill Clinton, made the case for his wife's presidency, calling her the "best darn change-maker I've ever known".
"Hillary opened my eyes to a whole new world of public service by private citizens," he said.
In other key moments on Tuesday:
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