All five living former presidents - Barack Obama, George W. Bush, Bill Clinton, George H.W. Bush and Jimmy Carter - paid tribute to the courage and character of McCain who died of brain cancer on Saturday aged 81.
Vice-president Mike Pence is likely to attend, said the officials, who spoke on condition of anonymity to describe private discussions.
The American flag flying above the White House was at full-staff early Monday morning even as the nation continued honoring the life and legacy of Sen.
And when an October 2017 interview turned to the subject of service in the Vietnam War - a profoundly marking experience in McCain's own life - he did not hold back.
Jim Roddey, former chairman of the Republican Committee of Allegheny County who campaigned for McCain during his 2008 presidential bid, referenced numerous same qualities.
The Arizona senator died at a time he saw as dark in the country's history, said John Weaver, a former aide and a longtime friend.
Obama, who triumphed over McCain in 2008, said that despite their differences, McCain and he shared a "fidelity to something higher - the ideals for which generations of Americans and immigrants alike have fought, marched, and sacrificed".
President Reuven Rivlin called McCain a "great leader, a defender of his people, a man of strong values, and a true supporter of Israel".
Ms Ward appeared to agree, replying: "I think they wanted to have a particular narrative that they hope is negative to me".
McCain is expected to be remembered at ceremonies in Arizona and Washington this coming week or next, if the family prefers to give more time for Congress to return to the Capitol from its summer recess. Plans call for McCain, a former Navy pilot, to be buried Sunday in the cemetery on the grounds of the U.S. Naval Academy in Annapolis.
He left Washington in December past year to spend more time with his family. "I found him to be an incredibly gracious and grateful person for this country".
Pennsylvania GOP Chairman Val DiGiorgio said McCain was "the epitome of a self-sacrificing public servant and an American hero" and "a family man of great integrity". I will always treasure the constant friendship he showed to the people of Israel and to me personally.
Senate Majority Leader Mitch McConnell said the Vietnam POW "showed us that boundless patriotism and self-sacrifice are not outdated concepts or clichés, but the building blocks of an extraordinary life".
Veterans who fought in the war were among those who travelled to the USA embassy in Hanoi to pay their respects.