Luke 7:3

And when he heard concerning Jesus, he sent unto him elders of the Jews, asking him that he would come and save his servant.

And when he heard ... What is more likely than the supposition that this centurion had heard from his fellow officer in the same city of the healing of a son; and that both were familiar with the healing of the nobleman's son in the same city? A vast number of Jesus' deeds were wrought in Capernaum (Matthew 11:23). The "hearing" would also have included the very words and attitude by which the first centurion had approached the Lord; and the second would have adopted the approach which was so successful with the first.

The elders ... In this appears one of the differences in the two similar miracles. The first centurion was a heathen; this one was evidently some kind of proselyte to Judaism; for it is hard to believe that he would have built the Jews a synagogue unless he was a follower of Judaism. This officer enlisted the elders of the people to convey his request to the Lord; in the case in Matthew, the centurion himself went to Jesus and made the request.