This is a fairly straightforward question where the answer becomes immediately obvious when looking at the first half of this mini-parable. The context is Jesus himself, and the comparison of himself “I” to a hen, comes straight after the threat from the fox Herod Antipas to kill him. Herod Antipas had only recently killed John the Baptist, and had been trying to see Jesus already since hearing about him (Luke 9:7-9) so the threat from Herod to Jesus in Luke 13:31 that Herod wanted to kill Jesus had been gathering for some time. Ultimately of course Herod Antipas would be part of the crucifixion of Jesus. Herod Antipas was in charge of one of the sequence of trials at which Jesus appeared during the night before the crucifixion – before Annas, Caiaphas, the Sanhedrin, Pilate, then to Herod, and finally Pilate again and the choice of Barabbas by the people.
31 At that time some Pharisees came to Jesus and said to him, “Leave this place and go somewhere else. Herod wants to kill you.” 32 He replied, “Go tell that fox, ‘I will keep on driving out demons and healing people today and tomorrow, and on the third day I will reach my goal.’ 33 In any case, I must press on today and tomorrow and the next day—for surely no prophet can die outside Jerusalem! 34 “Jerusalem, Jerusalem, you who kill the prophets and stone those sent to you, how often I have longed to gather your children together, as a hen gathers her chicks under her wings, and you were not willing. 35 Look, your house is left to you desolate. I tell you, you will not see me again until you say, ‘Blessed is he who comes in the name of the Lord’. (Luke 13:31-35)
Although it sounds almost as if Jesus is looking back over the history of Israel, the hen here is clearly Jesus not God. As much as God would want to gather the children of Jerusalem, the image of a fox trying to kill a hen would not be appropriate to Herod and God, but only to Herod and Jesus.