Strong weekend Mega Millions ticket sales easily could push Tuesday's jackpot above last year's record $656 million prize, a lottery official said.
No ticket matched the six numbers needed to win Friday's $425 million prize. It was raised Monday to $586 million for Tuesday's drawing - the fourth largest in U.S. history.
The estimated cash value of the jackpot is $316.5 million.
Oklahoma and Kansas are two of 43 states which participate in the Mega Millions lottery.
The record jackpot was shared by players in Illinois, Kansas and Maryland on March 30, 2012.
Tuesday's Mega Millions drawing is scheduled for 9:59 p.m.
The Associated Press contributed to this report.