In a post on the blog Right Reason, Glenn Peoples seeks to make the case that Paul quotes from the Gospel of Luke.
The reference is to the connection between 1 Timothy 5:17–18 and Luke 10:7.
If one were to make the case that the Pastoral Epistles were by Paul, despite the implausibility, then it could still be a case of Paul remembering a saying of Jesus and blurring it with what the Jewish Scriptures said. After all, Jesus was a Jewish teacher, and so it should not surprise us to find that much of what is attributed to him is not unique, but a way of understanding the Jewish Scriptures.
More likely scenarios, however, take seriously the evidence that (1) Paul did not write 1 Timothy, and (2) Luke is quite possibly the last of the Gospels to be written, perhaps later even than Papias.
But 1 Timothy could be later still.
And so which seems more likely to you? That the author of 1 Timothy was influenced by the Gospel of Luke? That the Gospel of Luke was influenced by 1 Timothy? Or that both reflect knowledge of oral tradition which attributed this saying to Jesus?