While an audience with the Pope is a highlight for most pilgrims, Leo XIV does not feature in the Brotherhood's pilgrimage programme. The reason: their status under canon law is unclear. Talks to reach an agreement have always failed, sometimes at the last moment.
However, it was the last jubilee year in 2000 that provided the impetus for a small rapprochement. Will it be the same this time?
There is currently growing pressure within the traditionalist community to seek a compromise with the Vatican. The conservative association is not suffering from a lack of young priests.
But it lacks bishops for ordination. Of the four bishops consecrated without authorisation in 1988, two remain: the Swiss Bernard Fellay (born in 1958) and the Spaniard Alfonso de Galarreta (born in 1957), who has recently suffered from ill health.
They are joined by numerous branches of the association worldwide as well as four seminaries in Germany, Switzerland, Argentina and the USA. Young men are trained there and ordained first as subdeacons, then as deacons and then as priests. However, only a bishop can do this in the Catholic Church.
Break with Rome and missed opportunities
This also applies to the ordination of bishops. It was this that led to the final break between the Fraternity of St Pius X and the Pope in Rome in 1988.
The community was formed around the French Archbishop Marcel Lefebvre (1905-1991), who rejected the modernisation of the Catholic Church decided by the Second Vatican Council (1962-1965).
Five years after the founding of the Priestly Fraternity in 1970, the Vatican withdrew the canonical legitimisation of the Fraternity, and a year later Lefebvre lost his episcopal rights.
Despite a papal ban, he first ordained priests and then Fellay, de Galarreta, Bernard Tissier de Mallerais and Richard Williamson as bishops. All those involved were excommunicated.
Although Pope Benedict XVI lifted the excommunication in 2009, no agreement was subsequently reached.
De Mallerais died last October, Williamson, who had already been expelled from the Fraternity of St Pius X in 2012 for Holocaust denial, died in January of this year.
New bishops are now needed to ensure the continued existence of the community without running the risk of being excommunicated again. It is not known whether talks have been held with Pope Francis, who died in April, to this end.
Internal sources speak of a missed opportunity not to have obtained at least unofficial authorisation for episcopal ordinations from Francis. There were some rapprochements under him, as well as personal contacts.
Now a new pope is at the helm.
But it is highly questionable whether Leo XIV, who acted so cautiously, will want to burn his fingers on this hot potato within the Church at the beginning of his pontificate.
4,000 participants on pilgrimage to Rome
The community will be present in Rome these days outside of papal audiences; the city is expecting around 4,000 participants: on Tuesday in the papal basilica of Santa Maria Maggiore, where Pope Francis is buried.
On Wednesday, a mass celebrated by Superior General Davide Pagliarani will be followed by a visit to the Basilica of St John Lateran, the Pope's seat as Bishop of Rome. This will be followed on Thursday by a walk from Castel Sant'Angelo to St Peter's Basilica.
Officially, this is the only appointment of the Fraternity of St Pius X in the Vatican.