To win the jackpot, a ticket holder has to match all numbers on five white balls and one red ball selected at the twice weekly Powerball draw -- next due on Wednesday at 10:59 pm (0359 GMT Thursday).
The winner can choose to be paid the full jackpot in annual installments over 29 years -- or take a one-off cash payment of USD 930 million -- before taxes.
At the last draw on Saturday, 25 people matched the first five numbers -- winning USD 1 million each -- and three others had paid a bonus netting them USD 2 million each but no one claimed the then USD 950 million jackpot.
Grief said sales were record breaking and could not rule out that the jackpot would again rise before Wednesday's draw.
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"I'm hearing anecdotally and through news outlets, millions of people who have never played Powerball before are indeed purchasing a ticket," said Grief.
Some retailers scoring the biggest sales are in states bordering the handful that do not participate in the Powerball, he said.
"People are flocking over from those states to stand in line and buy lottery tickets," he said. "You do not have to be a citizen of the US, people are coming from Mexico and Canada to purchase tickets," he added.
The world's richest lottery is Spain's annual Christmas "El Gordo," which in 2015 handed out 2.2 billion euros ($2.4 billion) but which capped individual wins at 400,000 euros and handed out thousands of smaller prizes.