What is the basis for the belief that Ignatius of Antioch knew the Apostle John?

What is the basis for the belief that Ignatius of Antioch knew the Apostle John? This seems to be a traditional belief. For example, The Catholic Encyclopedia entry from 1910 says > "It is also believed, and with great probability, that, with his > friend Polycarp, he was among the auditors of the Apostle St. John." Yet it gives no explicit reason why it is believed with great probability. A Q & A answerer here says > "Ignatius of Antioch doesn't mention any personal connection to John > in his authentic letters. Irenaeus mentions that he met Polycarp, who > had known John and at least one other apostle, as he refers to > "apostles" in the plural being known to Polycarp (Against Heresies > 3.3). Ignatius did write letters to Polycarp and to the church at Smyrna. There are two letters of Ignatius to John preserved in Latin, > but these are universally recognized as forgeries dated to the middle > ages. **There's no reliable evidence to connect Ignatius directly with > any of the apostles. So, as you say, this is likely a case of > "tradition based on forgery."**" Is this correct - is the idea that Ignatius of Antioch knew the Apostle John based solely on forged letters?