Exegesis:
dio oude emauton ēxiōsa pros se elthein ‘nor, therefore, did I consider myself worthy to come to you.’ For dio cf. on 1.35. oude is a continuation of ou in the preceding clause and goes with ēxiōsa. elthein means here implicitly ‘to come in person’ (cf. New English Bible).
axioō ‘to consider worthy.’
alla eipe logō lit. ‘but say, or, command with (only) a word,’ hence ‘say (only) a word,’ or ‘just say the word,’ or “just give the order” (Phillips). For eipe meaning ‘command.’ The clause implies that Jesus’ personal presence is not necessary to heal the slave. It is sufficient when he speaks a word from a distance.
kai iathētō ho pais mou ‘and let my slave be healed’ (imperative, third person). This imperative is the word which the centurion wants Jesus to speak and, by saying it himself, he, as it were, anticipates Jesus’ saying it. For pais cf. on 1.54; here it is synonymous with doulos (vv. 2, 10), though it sounds slightly more friendly.
Translation:
Therefore I did not, preferably, ‘therefore also I did not…,’ ‘that also caused me not to….’
Come to you, or, “approach you” (New English Bible), or very humbly, ‘show myself in your presence (lit. approach the dust on your feet)’ (Balinese).
And let my servant be healed. This difficult form may be rendered as a request, ‘and, please, heal my servant,’ or as an utterance of confidence, cf. “and my servant will be cured” (New English Bible); the former is preferable though the latter is acceptable also. Or again, making explicit the implied direct discourse, one may use something like, ‘and, please, say, “I want your servant to be well (again)” .’
Servant, see on 12.37. Sometimes differentiation from ‘slave’ in v. 2 is possible, e.g. ‘boy’ (Sranan Tongo, similarly Bahasa Indonesia KB), but often the two renderings have to coincide.
Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.