The Ronald Reagan Presidential Foundation reportedly bought the greenbelt area from the Cornerstone Community Church, which was asking for $7.2 million for the property.
The land is being purchased to preserve the views from the Air Force One Pavilion at the library.
A foundation spokesperson said the sale was set to be final in July.
The foundation has embarked on a "Save Our View" fundraising campaign to help with the purchase of the property.
The Associated Press contributed to this report.