He does not actually ask for forgiveness but his naming Christ in the final scene before the devils come and take him to hell is like a prayer that won't be listened to since the "deed of gift" is binding : "Rend not my heart for naming of my Christ." (Act V, scene 3). As a matter-of-fact, the devil threatened to tear him into pieces if he named God (Act V, scene 2).
He is certain to be damned even though he is striving toward salvation. However, he cannot help wishing to be turned into another being, a brutish beast, that has no soul, rather than face the irrevocable. His conscience is confined to the mere consciousness that the end is drawing nearer and nearer. There's no sense of guilt, no real pang of consciousness as regards the past, just the nagging feeling that death and damnation await him. There's no selflessness despite a true but fleeting feeling of love and devotion toward God.
Let's notice that only in the last minute does Faustus propose burning his books after he has yielded to despair. As the good angel said: "the jaws of hell are open to receive thee." (V.2. 118).