Both gay and straight men and women training to join the priesthood should face the same questions about their lifestyle, a report by the House of Bishops to be presented to the Church's General Synod next month will say.
Singling out homosexual applicants is seen as "pastorally unhelpful", it will add.
The term is a reference to the former US military policy between 1994 and 2011 which barred openly gay or bisexual Americans from serving but did not discriminate against them if they did not disclose their sexuality.
The recommendation formed part of the wider report, which also suggested the Church should adopt a "fresh tone and culture of welcome and support" for gay people - but not change its opposition to same-sex marriage.
The Rt Rev Graham James, Bishop of Norwich, said: "It's felt there is too much concentration on whether ordinands (priests in training) or clergy are in sexually-active same-sex relationships, rather than framing questions about sexual morality within a much wider examination of the way in which all ordinands and clergy order their lives.
"The Church of England has always been suspicious of intrusive interrogation of its members, preferring to trust clergy and lay people in their Christian discipleship.
"However, all clergy are asked at their ordination whether they will fashion their lives 'after the way of Christ'.
"This is not Don't Ask, Don't Tell in any shape or form."
The report will be presented to the four-day Synod, which starts on February 13.
New teachings on marriage and relationships should also be drawn up to replace those introduced in the 1990s, it suggests.
Church law and guidance on marriage should be interpreted in a way that provides "maximum freedom" for homosexuals, it added.
Canon Jeremy Pemberton, a hospital chaplain in Lincolnshire, tied the knot with long-term partner Laurence Cunnington.