DiNardo, of the archdiocese of Galveston-Houston in Texas, requested the meeting with the pontiff as the Catholic Church in the USA faces clerical sex abuse scandals on several fronts.
In Cardinal Wuerl's letter to the priests, which was obtained by LifeSiteNews and confirmed by the Archdiocese of Washington that it was sent on Tuesday, he discusses a resignation letter that he submitted in November 2015.
Francis will on Thursday meet leaders of the US Catholic Church, including their president Daniel DiNardo, who said last month he was eager to meet the pope following the scandal.
In an explosive 11-page letter, Archbishop Viganò, the former apostolic nuncio to the United States, accused Pope Francis of lifting sanctions that were placed upon the former D.C. Cardinal McCarrick during Pope Benedict's reign, going so far to making him a close adviser.
DiNardo has also said recent accusations that top Vatican officials - including the current Pope - covered up for McCarrick since 2000 deserve answers.
Following his prolonged silence on the matter, the pope's advisors announced Monday that he is preparing a statement on Viganò's claims. "He tries to uncover the sins, so they are visible in order to scandalise the people".
While Francis has often talked about sexual crimes as an abuse of power, some conservatives say the Pope has downplayed the role of homosexuality among priests while instead signalling a slightly more inclusive stance about gays within the church.
Moving priests who have been accused of child sex abuse is widely seen as a way to help them avoid facing any consequences.
Last week, one protester yelled "shame on you" at him, and another turned her back during a service.
The Pope upset many Catholics Tuesday when, rather than addressing the horrific sexual abuse and cover-ups by Catholic bishops, he preached a homily saying "the Great Accuser" was attacking bishops to create scandal. He accepted Barros's resignation in June.
Wuerl's name was mentioned several times in the report for allegedly not doing enough to remove some predator priests from ministry.
Amid such turmoil, a gathering of the global church leadership to discuss a specific problem - in the tradition of church synods and councils - is a good idea, but should take place sooner than February, said Christopher Bellitto, a church historian at Kean University in New Jersey.