No, Satan cannot and will not repent of his sin. The devil cannot be saved. First of all, Satan is completely fallen and is given over to evil. There is no room in his heart for repentance. Second, since must be atoned for and angels have no atoning sacrifice. The sacrifice of Christ on the cross is for people, not for angels. What is important to understand is that in the one person of Jesus are two natures, God and man. As God the Son, Jesus can offer a sacrifice that can appease God the Father. As a man, he can offer a sacrifice on behalf of men. This is why we are able to be saved. The atonement of Christ is offered on our behalf.
Therefore, even if Satan were to repent of his great sins, (which it is not possible) he must have an atonement that would be sufficient for angels. Since Jesus became a man to die for men, there would have to be some sort of corresponding angelic manifestation on behalf of the Divine Word becoming angelic. This is not taught in Scripture and does not seem to be possible.
Our sins are against God. Our sins have offended God and we need a way to undo the offense. We need to have a way to make amends. Biblically, this is done through atonement, where a death is involved (Leviticus 17:11; Hebrews 9:22) to undo the death that is due us. God tells us that the wages of sin is death (Romans 6:23), and that sin separates us from God (Isaiah 59:2).
For us, the atonement is the offering of Jesus on the cross (1 Peter 2:24).
However, there is no atonement for the angelic realm.
Heb. 2.16-17, “For assuredly He does not give help to angels, but He gives help to the descendant of Abraham. 17 Therefore, He had to be made like His brethren in all things, that He might become a merciful and faithful high priest in things pertaining to God, to make propitiation for the sins of the people.”
Therefore, since the Bible tells us there is no help for angels, which means there is no atonement for them, then fallen angels, the devil included, cannot be saved.
