Looking at the verses in context, I would say that age is not implied. First, the context is different in each case so I will take them by instance.
- Matthew 10:23-25
22 and you will be hated by all for my name’s sake...
24 “A disciple is not above his
teacher, nor a servant above his master. 25 It is enough for the
disciple to be like his teacher, and the servant like his master. If
they have called the master of the house Beelzebul, how much more will
they malign those of his household.
Notice that the Jesus uses v.24 as a parallel to v.25 which together constitute his reasoning for v.22. The main idea is that if the people are persecuting Jesus for teaching what he teaches, then his disciples can expect the same treatment. Thus "above" means the difference between outsiders treatment of Jesus(the master) and the disciples(his servants).
- Luke 6:39-40
39 He also told them a parable: “Can a blind man lead a blind man? Will they not both fall into a pit? 40 A disciple is not above his teacher, but everyone when he is fully trained will be like his teacher.
Once again Jesus is using a parallel but for a different end. The implication is that a teacher is a person who claims to "see" what his disciples do not and "leads" them into his knowledge. If one person leads another, both will end up in the same place, good or bad. Here the "above" is focused on the difference in knowledge of the teacher and student.
- Luke 19:39
38 saying, “Blessed is the King who comes in the name of the Lord! Peace in heaven and glory in the highest!” 39 And some of the Pharisees in the crowd said to him, “Teacher, rebuke your disciples.”
I'm not sure how the teacher-disciple relationship here could imply an age difference. The terms relate to authority, but aside from the fact that older people are often considered wiser, there is nothing to suggest the Pharisees meant anything other than an authoritative relationship. The intent was for Jesus to stop his disciples from equating him with Yahweh.
***All scripture quoted from ESV