Robert Hamilton makes a very good case that passages such as John 10:26 'you do not believe, because you are not my sheep' refers primarily to the faithful sons of Abraham who were God’s children under the covenant as it was revealed in the Old Testament, and who were already prepared by their voluntary faith and repentance to embrace the promised Messiah. (link)
Hamilton starts out by distinguishing between necessary and sufficient conditions for salvation in the Gospel of John. First, there are the necessary conditions of being “enabled” to come to Christ and being “drawn” to him by the Father (6:44, 65). Necessary conditions are signaled in the passages above by the grammatical structure “No one can . . . unless . . .” Second, we find in the above passages from John’s Gospel the sufficient conditions of being “given” to Jesus by the Father, having “listened to” and “learned from” the Father, “belonging” to God (i.e., being his child, cf. the contrast to the children of the devil in 8:44), and being one of Jesus’ “sheep” (6:37, 45; 8:47; 10:26, 29; 17:6, 9, 24). Sufficient conditions are generally signaled by phrases such as “Everyone who . . .” (6:45; Greek pas ho . . .) or “All that . . . will . . .” (6:37; Greek pan ho . . .), indicating that every person without exception who meets the relevant conditions will experience the result entailed by those conditions. The focus of Hamilton's essay are the passages addressing the sufficient conditions for salvation.
Hamilton pours through the scriptures in explaining that in the OT the nation of Israel were God's 'people' and His 'sheep' and His 'children'. In another more restrictive sense those who are in a right covenant relationship with God are His people, sheep and children, and that covenant relationship is conditional based on repentance and faith. Also, John the Baptist makes ready a people prepared for the Lord. So the Gospel of John deals with Jews who had responded favorably to the prevenient grace extended to them by God under the covenant as it was revealed in the Old Testament. Hamilton also explains they had already made the free choice to be “on the side of truth” (18:37) and to yield themselves in repentance and loyalty to God. Consequently, God could, by the inner working of his Holy Spirit in their hearts, direct all of these faithful ones who already belonged to him to embrace Jesus, the Messiah-Shepherd, as the new focal-point of their faith and loyalty.
This demonstrates one of the main themes of the Gospel of John, the union between the Father and the Son, by answering and important doubt: did the leaders’ rejection of Jesus indicate that he was, in fact, not sent from God to shepherd the flock of Israel? On the contrary, Christ is the Father’s sole aim in the dispensing of prevenient grace.
Hamilton also touches on how this idea relates to the gentiles, Acts 13:48, Cornelius and a number of other texts in the Gospel of John.