The immediate difficulty here is that Moses never did say anything specific about Jesus that we have recorded in the Bible. But the correlation between Moses and Jesus is remarkable. And it is also worth noting that Moses looked forward to God’s redemption and salvation of Israel through sacrifice. The whole of Leviticus, in fact, points to Jesus… as does Exodus… and Deuteronomy… and Numbers… and Genesis. Moses was close to God and it would seem in reading his experiences with The Great I AM that Moses was aware of God’s desire to act personally to save his people. Moses was a witness to God’s character and God’s love and God’s action for his people. Even in this general way, Moses was a witness to "God saves" (which is the meaning of "Jesus").
But it seems that Jesus has something even more specific in mind. Perhaps he was referring to his transfiguration- a mysterious encounter where Moses and Elijah appear with Jesus in front of three of disciples (Mark 9).
On top of this we see the correlation between how God used Moses to lead the people to freedom and how God used Moses to provide daily bread in the dessert. The manna (which means "What is it?") that God gave everyday to the Israelites was a sign of God’s provision for the people (Exodus 16:15). The future expectation of Israel was that the Messiah would come and "restore the manna to Israel (Nehemiah 9:15, Psalm 78:24). One ancient Jewish writing says "As the first Redeemer brough down teh manna… so will also the last Redeemer cause the manna to come down" (Midrash Qoh. 1:9)
In Exodus 16, the people were grumbling about the difficult conditions they found themselves in. Some wanted to go back to Egypt! So they directed their complaints at Moses and Aaron… but Moses and Aaron made it clear that their complaints were really against God. So in response, God gave them manna and to test them – to see if they would really follow him.
So, when the people are hungry in John 6, Jesus feeds them… thousands of them… with practically nothing. It’s interesting that shortly after this, the people grumble against Jesus and demand a sign. "Do something spectacular," they demand, "like Moses did!"
- Grumbling at God was characteristic of those wandering in the wilderness… In a span of three chapters in Exodus, they grumbled about the water God gave them (Ex 15:24), about not having enough bread (Ex 16:2), about not having enough water (Ex 17:3), about their hardships (Num 11:1), and even against the manna (Num 11:4-6). God considers the grumbling as a rejection of Him.
- Eating God’s word is a frequent metaphor in the Bible. Eg. see Isaiah 55.