Jesus said in John 10:30:  "I and the Father are one.”

" 23And He was saying to them, “You are from below, I am from above; you are of this world, I am not of this world. 24Therefore I said to you that you will die in your sins; for unless you believe that I am He, you will die in your sins.” 25So they were saying to Him, “Who are You?” Jesus said to them, “What have I been saying to you from the beginning? 26I have many things to speak and to judge concerning you, but He who sent Me is true; and the things which I heard from Him, these I speak to the world.” 27They did not realize that He had been speaking to them about the Father. 28So Jesus said, “When you lift up the Son of Man, then you will know that I am He, and I do nothing on My own initiative, but I speak these things as the Father taught Me." (John 8:23-28).  

Every time, in this passage, that Jesus says "I am He," the original text says just "I am.  When Moses met God at the burning bush, he asked God who should I say is sending me and God referred to Himself as "I am."  In this passage, by saying "I am" twice, He is claiming to be God.

Similarly in John 8:58, "Jesus said to them, “Truly, truly, I say to you, before Abraham was born, I am.”"  

Here Jesus is referring to His Godhead and His eternality.

Jesus does not leave us the option of calling Him anything less than God.