Theophylact of Ohrid

Why then does Peter not ask the Lord himself, but gives a sign to John? In many cases Peter, out of great fervor, was impetuous, but was subjected to reproach. Therefore now he was afraid to ask, lest the Lord once again rebuke him as being impulsive.

Commentary on John ↗

Augustine of Hippo

Observe too his mode of speaking, which was not by word, but by beckoning; Beckoned and spake, i. e. spake by beckoning. If even thoughts speak, as when it is said, They spake among themselves, much more may beckonings, which are a kind of outward expression of our thoughts.

Catena Aurea by Aquinas ↗

Thomas Aquinas

Then when he says, so Simon Peter beckoned to him, John mentions what led him to question Christ. But since to beckon is to suggest something without speaking any words, why does he say that Peter both beckoned...and said? I answer that the word beckon can also mean just to think something within ourselves, as "The fool says in his heart..." (Ps 53:1). And, even more so, we can say that someone said something when he indicates by some external sign or gesture what he has conceived in his heart. …

Commentary on John ↗

Bonaventure

Simon Peter therefore beckoned to him and said to him: Who is it of whom he speaks? As if to say: ask him. Peter was always eager to inquire, both by himself and through others. At Peter's request, that disciple inquires.

Commentary on John, Chapter 13 ↗