Stops will include a visit to Ground Zero and Washington, where they'll dine at the White House, says Britain's Sunday Telegraph.
"They are grateful the president is being so hospitable towards them," a senior U.S. official told the newspaper.
It would be the prince's first official visit to the White House since 1985.
The White House refused last night to confirm or deny the dinner plans.
While in Washington, Charles and Camilla will skip the usual four-star hotels in the capitol to stay at the home of British Ambassador Sir David Manning (search).
The 10-day trip, which is to begin the last week of October, will also include a stop in San Francisco.