But changes thought to be put to the Church’s parliament, general synod, next month, would remove this requirement.
Gay clergy would still be expected to adhere to the Church’s teaching that intercourse should only be in heterosexual marriage, but their superiors, according to the Sunday Times, will not question them on it.
It follows similar claims by the Mail On Sunday in December.
The Church’s House of Bishops will meet on Monday and are expected to finalise the proposals before they are bought before synod in February.
They are thought to emphasise that gay Christians must be fully welcomed but not move to change the current ban on gay blessings on marriages in church.
The proposal comes as the next stage in a long and divisive debate over sexuality after Parliament legalised gay marriage in 2013.