I started Bart Ehrman's 1993 book, The Orthodox Corruption of Scripture: The Effect of Early Christological Controversies on the Text of the New Testament. On page 22, we read:
"Clement of Alexandria reports in his Stromata
that Valentinus was a disciple of Theudas, allegedly a follower of
Paul, and that Basilides studied under Glaukia, a supposed disciple of
Peter (Strom. 7, 17, 106)."
You can see here what Clement says. Clement appears to be rather skeptical about these claims.
Gnostic Christians were claiming that some of their leaders had
connections with someone who knew the disciples. Some Catholics like to
tell me that I should trust certain church fathers because they studied
under a disciple of Jesus. But Gnostic Christians made a similar claim
about their leaders (though, to be fair, at least according to Clement,
their claim was that their leader studied under a disciple of a
disciple of Jesus). Why trust one but not the other?
I'd be very
hesitant to say that the disciples of Jesus were Gnostic (or
proto-Gnostic) Christians. But I also question to what extent we should
accept any Christian community's claim to have a connection with the
disciples, since all sorts of communities apparently made that claim.