The Italian was last month forced to release a statement a few days into his tenure at the Stadium of Light saying he does "not support the ideology of fascism" because of intense focus on past statements he had made.
Di Canio met with club owner Ellis Short to discuss the matter.
"I told him, 'Tell me what I have to do. Bye bye. No problem, because I do not want to be a problem for the club'," Di Canio told the Independent on Sunday.
"'If I don't represent a problem for you I am okay, I am ready to handle the pressure. It is no pressure for me. All day rubbish me, I don't care. It is my life, but if you think 'mmm, probably yeah, I let you be free', I don't want nothing and I go'.
"He said, 'Absolutely, you have to stay. You are our man.'
"That for me was enough. Refocus. I will never forget what he did. He gave me a big chance of my dream to become manager at the top level. Next year I hope I can be here. You never know what is going on in life.
"In this moment, he did not give up, he gave me 100 per cent, 200 per cent support. He convinced me to stay because he said you are our man. He is the owner, he picked me. I can't forget for the rest of my life, no matter what happens in the future."
Sunderland sit three points clear of the relegation zone with two games remaining.