In a speech in Brazil in July, Francis appealed "to those in possession of greater resources," saying that they should "never tire of working for a more just world, marked by greater solidarity. No one can remain insensitive to the inequalities that persist in the world."
It was unclear when Dolan may speak with the individual donor.
Langone, who describes himself as a devout Catholic who prays every morning, said he has told the cardinal that "you get more with honey than with vinegar." He said he also wants to make clear that wealthy Americans are some of the biggest donors in the world.
"There is no nation on earth that is so forthcoming, so giving," he said, adding that he hopes the pope can "celebrate a positive point of view rather than focusing on the negative."
The United States ranks No. 1 in the Charities Aid Foundation's most recent World Giving Index, with proportionally more Americans giving than the population of any other country.
Dolan said that the pope has expressed gratitude for American philanthropy.
"In the one long sit-down that I had with him, the Holy Father told me that he has a lot of gratitude for the generosity of the Catholic Church in the United States. He's aware of our help to the missions, to the poor of the world, to international development, to peace and ... justice," he said. "So, I know that he's very grateful for the ... legendary generosity of the Catholic Church in the United States."
Langone said he is also on a campaign to explain "the vast difference between the pope's experience in Argentina and how we are in America."
(Read more: Blunt Pope Francis targets free-market economics)
Francis is from Argentina, a country that suffered tremendous economic upheaval in early 2001 in what was then the largest sovereign default in history. Poverty rates skyrocketed overnight when the country refused assistance from the International Monetary Fund.
Arthur Brooks, head of the American Enterprise Institute, a think tank that promotes free markets, said he agrees that the pope's beliefs are likely informed by his Argentine heritage.
"In places like Argentina, what they call free enterprise is a combination of socialism and crony capitalism," he said.
Brooks, also a practicing Catholic who has read the pope's exhortation in its original Spanish, said that "taken as a whole, the exhortation is good and right and beautiful. But it's limited in its understanding of economics from the American context." He noted that Francis "is not an economist and not an American."