The Wall Street Journal reported that Barr has known about the probes since at least the spring and worked to avoid their public disclosure during the election campaign.
The newspaper attributed its report on Thursday to a person familiar with the matter.
Barr’s decision to keep the lid on the probes came even as Republicans and President Donald Trump pressed him for months to pursue Joe Biden’s son.
But the Journal pointed out Justice Department guidelines caution investigators from taking any overt actions as an election nears so they are not seen as trying to influence the outcome.
On Thursday night, Trump blasted the FBI and the Department of Justice over the news that Hunter Biden is under federal investigation. He demanded to know why the probe wasn't announced before the November election.
According to The New York Times, the U.S. attorney's office in Delaware opened one investigation against Hunter Biden in late 2018, before his father became a presidential candidate. It includes inquiries into potential violations of money laundering and tax laws. Sources close to the investigation said the money laundering part of the case did not gain traction.
And the Journal reported that federal prosecutors in Manhattan had also been looking into Hunter Biden’s business and financial dealings. While Hunter Biden is implicated in that probe, he was never a target for criminal prosecution, the Journal reported.