I know Saint Ignatius didn't speak of the Church Of Rome as the center of catholicism, however other saints of the same century of him did.
from Saint Ignatius we can see that he never called himself "Patriarch", he describes Bishops, Presbiters and Deacons. but not nationalistic patriarchs.
From the Epistle of Ignatius to the Smyrnaeans:
See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid.
Now ¿where can we read or guess the idea of a patriarchs of national churches?