No, Satan cannot be saved. In order for him to be forgiven of his sins he must have an atonement. His sins are against God. Therefore, it is God who is offended. It is the same with us. 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). But what is important to understand is that Jesus has two natures: divine and human. In other words, 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 sacrifice on behalf of men. This is why we are able to be saved, because the atonement of Christ is offered on our behalf.
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. 17Therefore, 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.