The singer and his partner David Furnish, want to become parents to the 14-month-old toddler who they met during a visit to an orphanage with his AIDS charity foundation.
Sir Elton, 62, said he had always rejected the idea of adoption because of his age and because he regularly went on tour around the world.
But he said little Lev had "stolen his heart" and forced him to reconsider his original decision.
He said: "David and I have always talked about adoption, David always wanted to adopt a child and I always said 'no' because I am 62 and I think because of the travelling I do and the life I have, maybe it wouldn't be fair for the child.
"But having seen Lev today, I would love to adopt him. I don't know how we do that but he has stolen my heart. And he has stolen David's heart and it would be wonderful if we can have a home. I've changed my mind today."