All that the Father gives Me will come to Me, and the one who comes to Me I will certainly not cast out. For I have come down from heaven, not to do My own will, but the will of Him who sent Me. This is the will of Him who sent Me, that of all that He has given Me I lose nothing, but raise it up on the last day. For this is the will of My Father, that everyone who beholds the Son and believes in Him will have eternal life, and I Myself will raise him up on the last day. – John 6:37-40
Clearly the Father has chosen some to be given eternal life and has given them to the Son. If the Father has given them to the Son, they will come to Him.
No one can come to Me unless the Father who sent me draws him; and I will raise him up on the last day. – John 6:44
This last statement pretty much declares that unless God draws us we cannot come to Him. This coupled with the earlier statements indicate that the Father chooses who will and will not be saved. We cannot come to Jesus unless the Father draws us, and all whom the Father draws will be saved.
This says nothing about the criteria the Father chooses for whom he will draw to Jesus, but it does appear to indicate that it’s God that chooses, and not us.