The leper seeks healing from Jesus because he knows that a priest can pronounce him clean, but only Jesus can make him whole, since Jesus has come to fulfill, not just proclaim the Law and the Prophets (Matthew 5:17), including actually healing the leper and thus making him clean.
The leper is aware of the fact that, since Jesus came to fulfill the Law and the Prophets (Matthew 5:17), Jesus can do what no priest in the Old Testament could do, namely, to actually heal a leper. The priest could determine whether the person had been cleansed, and they had to confirm it with sacrifices and solemn ritual, but they could do nothing more than merely confirm a fact. This leper clearly believes that Jesus is more than Moses (Van Bruggen, page 136), and as such not only has the authority to pronounce him clean, but to actually heal him if he is willing to do so. Just like the work of creation, so too is the work of redemption exclusively dependent upon the will of God.1
2 And behold, a leper came to him and knelt before him, saying, “Lord, if you will, you can make me clean.”