Aides at the National Governors Association -- which Cuomo chairs -- have begun looking for contingencies to replace him, prompting speculation of his role within a Biden administration, Axios reported.
Democratic donors within Cuomo's orbit have reportedly told the outlet that Cuomo is being pushed for the attorney general job and that Biden is considering him for the role based on their decades-long friendship.
An attorney general within a Biden administration would be under political pressure to go after former Trump administration officials and manage nationwide unrest over police violence, among other pressing issues.
Biden's campaign team has declined to comment. Cuomo's office did not immediately respond to Fox News' request for comment.
Tim Murtaugh, Director of Communications for Trump's 2020 campaign, told Fox News: "There is zero chance that President Trump will appoint Gov. Cuomo attorney general in his second term."
Asked earlier this year by ABC's "Good Morning America" whether he would accept a potential Cabinet post within a Biden administration, Cuomo said he is content to remain Governor of New York.
"I was in a Cabinet, I was in Bill Clinton's Cabinet, been there, done that," Cuomo said, referring to when he was Secretary of Housing and Urban Development from 1997 to 2001. "I don't want to go to Washington. They couldn't drag me, they couldn't force me. I only represent the people of the state, I have no agenda besides theirs."
Cuomo's national profile was raised earlier this year for his handling of the coronavirus pandemic. But his favorability became mixed after he mandated in late March that coronavirus patients be sent to nursing homes from hospitals -- a decision widely blamed for nearly 6,000 deaths.
The mandate required nursing homes to take in patients so long as they were medically stable. The nursing homes were further prohibited from testing incoming residents for the virus before they arrived.
More than 6,300 COVID-positive patients were admitted to nursing homes between March 25 and May, according to a report from the New York state health department. The high number of admitted patients has been widely blamed for the state's official care home death toll of more than 6,600.
An analysis from the state health department determined that there was no causal link because "the timing of admissions versus fatalities shows that it could not be the driver of nursing home infections of fatalities."