UPDATE (4 Sept): Vatican spokesman Father Federico Lombardi has confirmed that Cardinal Müller and Bishop Fellay will meet later this month, but he didn't give a precise date.

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The prefect of the Congregation for the Doctrine of the Faith, Cardinal Gerhard Müller, is reportedly to meet the head of the breakaway Society of St. Pius X, Bishop Bernard Fellay, later this month.

According to the website TradiNews, the meeting, which is being billed as "informal", has been confirmed for Sept. 21st in Rome. 

If it goes ahead, it will be Cardinal Müller's first meeting with Bishop Fellay since his appointment as prefect. As head of the CDF, the German cardinal is also president of the Pontifical Commission Ecclesia Dei which is charged with helping to bring about reconciliation with the SSPX. TradiNews asserts that as Bishop of Regensburg, Cardinal Müller was clear in his opposition to the SSPX. 

Bishop Fellay has been to Rome at least once since Pope Francis' election, briefly exchanging greetings with the Holy Father in the Pope's Santa Marta residence last December.

In October 2013, he made a speech in which he described the Pope as a "genuine modernist" who is making a "real disaster" in the Church "10,000 times worse.” Speaking at the time, Cardinal George Pell said Bishop Fellay's comments were "absolute rubbish" and a "gigantic misreading" of the Pope. "Francis said he’s a loyal son of the Church, and his record shows that," he told La Stampa. 

Pope Benedict XVI launched a series of doctrinal discussions with the SSPX in 2009, lifting excommunications imposed on its four bishops in the hope they would return to full communion with the Church. The talks ended when the fraternity was unable accept the contents of a "doctrinal preamble" that outlined principles and criteria necessary to guarantee fidelity to the Church and its teaching.