Luke 7:8

‘For I also am a man set under authority, having under myself soldiers. And I say to this one, “Go”, and he goes; and to another, “Come”, and he comes; and to my servant, “Do this”, and he does it.'

He assured Jesus that he had no doubt that He could do this because he knew that He was a man who enjoyed the authority of God. So just as he himself could give orders and be obeyed, because he was a man under the rule of the powerful Caesar, and could act in his name, so he knew that Jesus could do the same with disease because He was under the authority of the Creator, and could act in His name. The centurion clearly had a high view of Jesus.