Deacons as Ordinary Ministers, and not Extraordinary, of Holy Communion [was] the common thinking at the time of Trent.
I can’t find any mention of it in the Sessions of the Council. Aquinas, writing in the 13th century (a few hundred years before Trent), says that the hands of the priest are consecrated so as to be permitted to touch the Blessed Sacrament (cf.
ST III, Q. 82, Art. 13); Michael Davies, a 20th century Catholic author, says that Aquinas witnesses to the fact that not even a deacon could touch the Blessed Sacrament with his hands “under normal circumstances” (
Privilege of the Ordained, p. 16).
As an aside, I find this (Session XXIII, ch. XVII, “In What Manner the Exercise of the Minor Orders Is to Be Restored”) interesting, in light of the post-conciliar elimination and reduction of the minor orders:
That the
functions of holy orders from the deacon to the porter, which have been
laudably received in the Church from the times of the Apostles, and which have been for some time discontinued in many localities,
may again be restored to use in accordance with the canons, and may not be
derided by the heretics as useless, the holy council, burning with the desire to
restore the ancient usage, decrees that in the future such functions shall not be exercised except by those constituted in these orders, and it exhorts in the Lord each and all prelates of the churches and commands them that they make it their care to restore these functions, so far as it can be conveniently done, in cathedral, collegiate and parochial churches of their diocese, if the number of people and the revenues of the church are able to bear it.