Some folks see similarities between the centurion of Luke 7 and the centurion, Cornelius, whom Luke mentions in Acts (cf. Acts 10:1-4). Besides their both being of the same rank in the military, they were both God-fearers (Acts 10:1). Both would have been aware of Jewish traditions of uncleanness associated with contact with non-Jews or gentiles (Acts 10:28). Both were generous with the wealth they had. The centurion seeking Jesus loved the Jews and built a synagogue for them (Luke 7:5), while the centurion who sent for Peter was noted for his love for the Jews and his generosity toward the Jewish people (Acts 10:2, 4, 22). Although these similarities don’t measure up to proof that the two are the same person, I believe it is probable they are one and the same person.
In any event, Luke tells us that a Roman centurion was seeking Jesus (Luke 7:3), because a beloved servant was sick and near death. The centurion had heard of Jesus and the miracles he had been doing for others concerning health issues. According to Luke, the centurion went to the Jewish elders of Capernaum, Jesus’ chosen home town. He sought their help in convincing Jesus to consider the request of a gentile for the dying young man, whose life he held dear (Luke 7:2). The same Greek word (entimos – G1784) is used in the Septuagint for David valuing Saul’s life (1Samuel 26:21).
Luke 7:3 may have a double meaning where the centurion comes to know of Jesus’ miracles and also comes to know Jesus had recently returned to Galilee from Judea (cf. John 4:45). Luke doesn’t say that the centurion had heard of Jesus’ miracles in Galilee prior to the Passover mentioned in John 2, but he may have. Another possibility, which may fit the context better, is that the centurion, probably coming from Caesarea, arrived in Capernaum with the nobleman’s sick son (cf. John 4:46). At this time he heard reports from the Jews, concerning what Jesus had done recently in Judea (cf. John 2:23), and immediately made his request to the local Jewish authorities to act on his behalf.
An objection may arise at this point in that Matthew presents a slightly different account of the same event (cf. Matthew 8:5-13). He doesn’t mention the Jewish mediators. Rather, he has the centurion speaking with Jesus face to face. Both Luke and Matthew are true, but Luke presents more of the details. The centurion makes a request of Jesus in both accounts, but Luke mentions how that request was made—i.e. through Jewish intermediaries.
An example of this difference in Matthew’s and Luke’s record can be found in how Paul relates his own account of being selected by Jesus as an apostle to the gentiles (Acts 9, 22 & 26)? In two accounts of Paul’s meeting with Jesus (Acts 9 & 22) an intermediary by the name of Ananias is mentioned as coming to Paul and relating what God had commanded him to do. However, when Paul relates those same events to King Agrippa in Acts 26, he leaves out the detail of Ananias’ coming to him with the word of God. Paul simply tells the king that God commanded him to preach the Gospel, as though there were no intermediary in the event at all. This detail was unimportant for Paul’s purpose of relating to the king what God commanded him to do.
Similarly, Matthew and Luke differ only in how the centurion makes his request known to Jesus. Luke records he used Jewish intermediaries; Matthew does not, but this cannot be construed to mean Matthew doesn’t know about the intermediaries. He simply doesn’t need them for the theme of his account of Jesus’ ministry.