The tickets were sold at a convenience store in suburban Phoenix and a gas station in Dearborn, Mo., just off Interstate 29, the highway linking Kansas City to the Canadian border.
Missouri lottery officials said they verified a ticket that was presented to them Thursday and set a news conference for 11 a.m. CST Friday at North Platte High School, near where the ticket was bought.
Lottery Chief Operations Officer Gary Gonder couldn't provide any details, including whether the ticket was bought by someone from Missouri.
Speculation had many of Dearborn's 500 residents buzzing about who had won.
Cashiers Kristi Williams and Kelly Blount greeted customers with big smiles and questions about whether they had bought the winning ticket. No one had come forward to claim the prize by late Thursday morning, Missouri Lottery officials said.
"It's just awesome," Williams said. "It's so exciting. We can't even work."
Karen Meyers, a server at the Cook's Corner Cafe, where the daily special was roast beef and potatoes, said she didn't believe it at first when she heard the winning ticket had been sold nearby.
"I think it's wonderful! I hope someone local won it, not someone just passing through," she said. "It's a small town where everyone is really nice."
Kevin Bryan bought his ticket at the Trex Mart and made an extra trip to his mother's home in Dearborn to verify that the ticket he left on her counter wasn't, in fact, the winner.
"When I heard it was sold here in Dearborn I about fell over," Bryan said, as he hung Christmas lights outside his mother's home.
He said the only other local lottery win he could remember was when an area farmer won about $100,000 in scratch-off game years ago "and bought himself a combine."
The winning ticket sold in Arizona was purchased at a 4 Sons Food Store in Fountain Hills near Phoenix, state lottery officials said. Customers poured into the store, to check their tickets and share in the big moment.
"I think it's crazy, and I also think it's great," said Bob Chebat, who manages the 4 Sons. "I'm glad that all that work yesterday wasn't for nothing."
The store was swept up in a nationwide ticket-buying spree preceding Wednesday's drawing, with the big money enticing many people who rarely, if ever, play the lottery to buy a shot at the payout.
Clerks at 4 Sons sold 986 Powerball tickets Wednesday, which Chebat said was well above average.
Baron Hartell, son of the owner of the Missouri store, said if the winner isn't a local resident it might have been a truck driver. Interstate 29 connects Kansas City to the Canadian border, so it's a busy thoroughfare in both directions.
"Even the truck drivers who come around, we see them every day, so they all feel like all locals to us," he said.
Store manager Chris Naurez said business had been "crazy" for Powerball tickets lately and that the store had sold about $27,000 worth of tickets in the last few days.
"This really puts Dearborn on the map," he said.
Kenny Gilbert, the general manager of Trex Mart, suggested his staff would be sharing in the $50,000 bounty that the store will be awarded for selling one of the winning tickets.
"The response from the owner was, 'I guess we'll be able to give out Christmas bonuses,'" Gilbert said. "That's nice, especially at this time of year."
Winners in both states have 180 days to claim their share of the prize money.
The numbers drawn Wednesday night were 5, 16, 22, 23, 29. The Powerball was 6. The $587.5 million payout represents the second-largest jackpot in U.S. history.
Tickets sold at a rate of 130,000 a minute nationwide - about six times the volume from a week ago. That pushed the jackpot even higher, said Chuck Strutt, executive director of the Multi-State Lottery Association. The jackpot rolled over 16 consecutive times without a winner.
Bob Kangas realized Wednesday night that one of two winning Powerball jackpot tickets had been bought in Arizona, but he didn't immediately check his numbers.
"I didn't want to look because I just wanted to dream about being rich," Kangas said Thursday while checking his tickets at the 4 Sons store where he bought his tickets - and where the winning ticket was sold.
"I just wanted to dream all night," he said, breathing a heavy sigh as he realized his tickets were not winners.
In a Mega Millions drawing in March, three ticket buyers shared a $656 million jackpot. This remains the largest lottery payout of all time.
Skoloff reported from Fountain Hills, Ariz.