I've also not been able to find a definitive attribution of this phrase to Pope Paul VI. Google Books has nothing helpful, and neither does a site search on vatican.va (I tried a few variations and keywords, in English and Latin).
However, I did discover evidence that the basic sentiment did not originate with him (whether or not he said that exact phrase at some point in his life). For example, this is from Picart's Religious ceremonies and customs (1723-1737) 1, as translated by William Burder (1841) 2 :
The Catholics look on the sacrifice of the mass as the most acceptable of all adorations, and the most effectual of all prayers. The Church not only prays herself at this sacrifice, which the priest offers up to God in the most solemn and majestic manner; but Jesus Christ also, by the sacrifice of his own body, is said to offer up to the Father the most perfect adoration that can possibly be paid to him, since it is offered by a God.
original: Nous devons expliquer un peu en détail les Ceremonies du Sacrifice de la Messe , que les Catholiques regardent comme la plus excellente de toute les adorations , & la plus efficace de toutes les prieres. Non seulement l'Eglise prie pour elle même à ce sacrifice, qu'un Prêtre offre à Dieu de la maniere la plus auguste que l'esprit humain ait pû concevoir; mais Jesus-Christ lui-même offre à son Pere par le sacrifice de son corps l'adoration la plus parfaite qu'on puisse lui rendre, puisqu'elle lui est rendue par un Dieu.
As with many other points of Catholic belief, we can turn to Saints Thomas Aquinas and Augustine of Hippo to learn more:
Saint Thomas defended the real presence of Christ in the Eucharist, and he brilliantly articulated the Church's understanding of the sacrifice of the Mass as the most perfect prayer of the Church.3
Aquinas' Summa Theologica contains a lot of material on these points. One relevant passage is II-II 83.17, where he discusses the "parts of prayer" - supplication, prayer, intercession, and thanksgiving - and notes that all are present in the rite of the Mass:
A gloss on 1 Timothy 2:1 says that "in the Mass, the consecration is preceded by supplication," in which certain sacred things are called to mind; that "prayers are in the consecration itself," in which especially the mind should be raised up to God; and that "intercessions are in the petitions that follow, and thanksgivings at the end."
The "gloss" he refers to is uncited here, but I think it is meant to point to one of Augustine's letters, sent to Saint Paulinus of Nola (Letter 149), which includes an extensive exegesis of 1 Timothy 2:1, the different forms of prayer named there, and their relations to the Mass. Elsewhere, Aquinas discusses how prayer and sacrifice are related as offerings to God, and records detailed observations about different prayers and other points of the Mass ceremony.
In summary, whether or not Paul VI said this, it's certainly the kind of thing he might have said! It's also worth noting that this idea depends on the Eucharist being a sacrifice, and not a memorial - otherwise it's not truly an "offering" according to Aquinas - so it's very much consistent with Catholic perception.
1. Cérémonies et coutumes religieuses de tous les peuples du monde representées par des figures dessinées de la main de Bernard Picard: avec une explication historique, & quelques dissertations curieuses. 7 vols. Amsterdam: J.F. Bernard, 1723-1737. Online at http://digital2.library.ucla.edu/picart. Quotation can be found at the bottom of vol. 1, p76.
2. Religious ceremonies and customs. William Burder. London. 1841. Page 205.
3. Prayer as a journey: Medieval spiritual paths. Christian Raab, OSB. In The tradition of Catholic prayer. Monks of Saint Meinrad Archabbey. 2007.