Two of the three sources CBS News cited said the vice president is leaning toward running.
Several Democratic donors who have met with Biden also told CBS News they came away with the impression that he would run. The sources say Biden will sit out the first Democratic primary debate Oct. 13 even if he announces his candidacy before then.
A spokesperson for the vice president did not comment to CBS News on the report.
A poll released earlier this week found Biden would be the most popular Democratic candidate if he entered the race.
Forecasters say Biden would likely take more support away from front-runner Hillary Clinton than surging candidate Sen. Bernie Sanders (I-Vt.), tightening the race for the Democratic nomination. (read more)