However, the Church has declined to officially respond to a government consultation on the issue as it does not hold a "settled view".
According to the Times, Rev Dr Malcolm Brown, the Church's director of mission and public affairs, said: "Trans people with gender recognition are already able to marry in our churches. Being transgender does not prevent someone offering themselves for ordained ministry and we have transgender clergy as well as laity.
"We can say with some confidence that excessive bureaucracy in the process of gaining a gender recognition certificate is neither welcoming nor affirming of transgender people...but we do not have a settled view in the Church of England about precisely which aspects of the legal process are necessary."
Politicians are asking whether the process should be simplified and made possible without approval from a doctor.
The Christian Medical Fellowship has responded to the consultation which ended on Friday.
Chief executive, Dr Peter Saunders, said: "Such a dangerous change would encourage the view that gender identity has nothing to do with a person's biological sex, it is a merely a social construct. This new ideological dogma has no evidence-base in science and self-declaration would appear to reinforce it as if proven fact.
"The Government is to be commended for seeking to reduce the burden of the process, and it might indeed be possible to improve aspects of the existing law, but removing sensible 'barriers' to overly-easy transition will result in more people embarking on early medical transition with insufficient thought, more people living to regret irreversible changes to their bodies and an overall increase in co-morbid mental health issues including suicide."
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