White House staff had suggested that an announcement could come as early as February but then pushed the possible date to April.
The latest reports are that Mr Biden may wait until the new campaign fundraising quarter begins in July in order to maximise the amount of time he can gather donations before having to disclose them publicly.
Quarterly fundraising totals are frequently viewed as an important indication of the strength of a campaign.
There are currently two announced candidates for the 2024 Democratic presidential nomination - best-selling self-help author Marianne Williamson and anti-vaccine activist Robert Kennedy Jr.
No prominent Democratic officeholders appear to be considering a challenge to the incumbent, however.
The lack of any formidable rivals in his party has given Mr Biden the ability to set the timing of any formal announcement without significant external pressure.
His advisers have said he sees an advantage in drawing a contrast between his role governing the nation while his potential Republican opponents engage in partisan campaigning or - in Donald Trump's case - deal with the fallout from a criminal indictment.
Last week, the former president pleaded not guilty in a Manhattan court to falsifying business records.
Behind the scenes, however, Mr Biden and his advisers are quietly assembling a campaign team and staffing the independent political action committee, Future Forward, that will provide financial support for the president's re-election effort.
At 80, Mr Biden is already the oldest president in US history. If he wins re-election, he will be 86 at the end of his second term.
