In Matthew 8:5-13 and Luke 7:2-10, we are told the story of the faithful centurion.
In the Matthew account, it makes it seem like the centurion talked personally to Jesus:
Matthew 8:5-13
5 And when Jesus was entered into Capernaum, there came unto him a centurion, beseeching him,
6 And saying, Lord, my servant lieth at home sick of the palsy, grievously tormented.
7 And Jesus saith unto him, I will come and heal him.
8 The centurion answered and said, Lord, I am not worthy that thou shouldest come under my roof: but speak the word only, and my servant shall be healed.
9 For I am a man under authority, having soldiers under me: and I say to this man, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it.
10 When Jesus heard it, he marvelled, and said to them that followed, Verily I say unto you, I have not found so great faith, no, not in Israel.
11 And I say unto you, That many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven.
12 But the children of the kingdom shall be cast out into outer darkness: there shall be weeping and gnashing of teeth.
13 And Jesus said unto the centurion, Go thy way; and as thou hast believed, so be it done unto thee. And his servant was healed in the selfsame hour.
The account in Luke, however, is clear in stating that the centurion never actually personally spoke to Jesus:
Luke 7:2-10
2 And a certain centurion's servant, who was dear unto him, was sick, and ready to die.
3 And when he heard of Jesus, he sent unto him the elders of the Jews, beseeching him that he would come and heal his servant.
4 And when they came to Jesus, they besought him instantly, saying, That he was worthy for whom he should do this:
5 For he loveth our nation, and he hath built us a synagogue.
6 Then Jesus went with them. And when he was now not far from the house, the centurion sent friends to him, saying unto him, Lord, trouble not thyself: for I am not worthy that thou shouldest enter under my roof:
7 Wherefore neither thought I myself worthy to come unto thee: but say in a word, and my servant shall be healed.
8 For I also am a man set under authority, having under me soldiers, and I say unto one, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it.
9 When Jesus heard these things, he marvelled at him, and turned him about, and said unto the people that followed him, I say unto you, I have not found so great faith, no, not in Israel.
10 And they that were sent, returning to the house, found the servant whole that had been sick.
The two passages don't have to contradict at all.
From Luke, we simply learn that the communication was accomplished via emissaries. The initial interaction, as well as the follow-up once the centurion hears that Jesus is on his way, were both done by messengers, something that Matthew doesn't mention. That doesn't make Matthew's account untrue.
Jesus truly spoke to the centurion, and vice-versa - via an emissary. This is functionally no different from message passing, or texting, both of which we would consider both parties to be talking to one another, even though it's not face-to-face.