That's according to The Wall Street Journal, which cites anonymous sources familiar with the deal.
Disney spokeswoman Leslie Goodman did not immediately return a phone call seeking comment. Major league baseball had not heard about a deal being reached.
"We haven't received anything final with anyone, and we know they are negotiating with that gentleman," Bob DuPuy, baseball's chief operating officer, told The Associated Press. "If and when they reach a final agreement, they would contact us. Nothing has been submitted."
The 56-year-old Moreno, a former minority investor in the Arizona Diamondbacks, would become the first Mexican-American to become majority owner of a major league team. According to Forbes magazine, Moreno has an estimated net worth of $940 million.
The Angels won the first World Series in their 42-year history last fall, but Disney has taken steep losses since becoming involved with the team seven years ago.
Disney bought a minority interest in the then-California Angels in 1996 from Gene Autry, who had owned the team since it joined the American League as an expansion franchise in 1961.
Disney acquired the rest of the team after Autry's death in 1998, paying a total of $147 million. The company also spent nearly $100 million to refurbish the team's stadium, renaming it Edison Field. It also signed a 33-year lease with Anaheim, with a clause that keeps the Angels in the city until at least 2017, even if Disney sells the team.
The idea was that Disney could promote its teams at its theme parks and tout those parks and other products at games. The cross-promotion was designed to keep tourists in Anaheim, but the strategy hasn't worked for the company.
Disney has been trying to sell the Angels and its other sports franchise, the NHL's Mighty Ducks of Anaheim, for several years.
The efforts intensified after the Angels won the World Series last year. Soon after the win, Disney Chairman and Chief Executive Michael Eisner said the company was being more aggressive about finding a buyer.
"The problem with a company like ours is, if you run them (sports teams) for the shareholders, you would have a negative impact on Disneyland and Orange County - you couldn't pay the salaries," Eisner said in November. "If you ran them for Orange County and Southern California, and pay what it takes for salaries, then you have the negative impact of losses."
By Mary Foster