DES MOINES, Iowa — America’s two biggest lottery games are talking about cross-selling tickets in U.S. lottery jurisdictions with the potential for a national lottery, the head of a lottery association said Tuesday.

Powerball is played in 31 states, the District of Columbia and the U.S. Virgin Islands. Mega Millions is played in 12 states. The consortium behind Mega Millions and the Urbandale, Iowa-based Multi-State Lottery Association, which runs Powerball, have agreed in principle to cross-sell tickets for both games beginning next year, officials said.

“It’s a way to increase sales and reach out to more players,” said Tom Shaheen, the president of the lottery association’s board of directors and executive director of the North Carolina Education Lottery.

The idea surfaced last year after officials noticed that when the jackpots grew, players who live in states offering Powerball would cross the border to buy tickets in another state selling Mega Millions and visa versa, Shaheen said.

Mega Millions drawings are held on Tuesdays and Fridays, while Powerball drawings are held on Wednesdays and Saturdays.

“This would be a wonderful opportunity for North Carolina players to participate in another large jackpot game,” Shaheen said in a statement. “In addition, it has the potential to increase funds raised for education.”

Cross-selling would give players the chance to buy whatever ticket they want in their home state, said Andi Brancato, a spokeswoman for the Michigan Lottery, which is a member of Mega Millions.

Shaheen said a national lottery is also in the works that would be in addition to Powerball and Mega Millions.

“If we develop a national game, it will probably be at a different price point. It might to $2. It might by $5. It will be a single game, but we haven’t worked out all the details of that yet. The other two games, I believe, would remain intact,” he said.

Cross-selling could begin in early 2010, and the organizations could begin a national lottery by next fall, said Multi-State Lottery Association executive director Chuck Strutt. The two groups will meet in the next few weeks to start working on the details, he said.

Shaheen said each state will have to decide if it wants to participate in cross-selling or join a national lottery.

Mega Millions holds the record for the largest U.S. lottery jackpot — $390 million on March 6, 2007. The largest Powerball jackpot was $365 million on Feb. 18, 2006.