But, according to the ancient sources, Peter requested that he be hung upside down because he didn’t consider himself worthy to die in a manner similar to our Lord’s crucifixion. From what I have read, the bones at St. Peter’s basilica are, in fact, those of St. Peter. I believe that as early as the time of Pope Pius XII, there was an archeological excavation (or, am I confusing that with the one at St. Paul’s Outside the Walls). In any case, I believe that there have been statements authenticating the bones located at St. Peter’s as those belonging to the Prince of the Apostles.
Nonetheless, regarding scriptural citations, the best that we can perhaps come up with is a previous poster’s citation of John’s post-Ressurection account (after Peter undoes his triple denial).
I would submit another observation which, although it has no concrete evidence, might seem plausible. John, the beloved disciple, wrote the fourth Gospel. Tradition has it that St. John outlived everyone else and died a natural death. It is possible (and don’t start thinking I’m crazy, but the question did make me think) that perhaps John inserted this interpretation (after Jesus’ statement) after St. Peter’s martyrdom. Again, this is not rooted in Tradition or theology; it’s just a hypothesis.