Not sure, off-hand, but there are some pretty old texts that attest to it. For instance there’s Tertullian: “For this is the manner in which the apostolic churches transmit their registers: as the church of Smyrna, which records that
Polycarp was placed therein by John; as also the church of Rome, which makes Clement to have been ordained in like manner by Peter.” (Tertullian,
Prescription Against Heretics, ca 200)
There are also the
Fragments of Papias (ca 110-140 AD) that indicate Papias knew both men: “Testimony is borne to these things in writing by Papias, an ancient man, who was a
hearer of John and a friend of Polycarp…”
In his
Epistle to the Ephesians, Ignatius speaks of knowing Polycarp: “I write to you, giving thanks unto the Lord, and loving
Polycarp even as I do you.”
There’s another mention in
Fragments of Irenaeus, who wrote around 170-180, that says Polycarp used to talk about conversations with John: “I can even describe the place where the blessed Polycarp used to sit and discourse— his going out, too, and his coming in— his general mode of life and personal appearance, together with the discourses which he delivered to the people; also how he would speak of his familiar
intercourse with John…”
Later, the early Church still attested to this, such as Jerome in
De Viris Illustribus: “Polycarp disciple of the apostle John…”