Rev Vivienne Faull says offering a blessing for gay couples is "not theologically a problem", and has urged the Church of England to revise its position on the matter.
In an interview with the Radio Times, Faull is currently Dean of York and may well become the first female bishop in the C of E should legislation pass in the House of Bishops this July.
She said the change in attitudes towards same-sex marriage had been "significant" in recent years, and that the Church needed to fully understand its changing context. She also compared the Church's policies on female bishops to its stance on homosexuality.
"I think it is very costly to the Church that women have not been able to be bishops till now - and this is also going to be costly. I'm getting approached by young people of the same gender planning their marriages," she revealed.
"They understand in their heads what the Church's position is, but they no longer understand in their hearts. It's driving people away and that's dreadful."
Rev Faull also shared that she has "found ways" of celebrating civil partnerships without flouting the Church of England's legislation.
"The blessing of a gay relationship is not theologically a problem for me personally, but I'm under the discipline of the Church and I keep the rules," she added.
A law allowing same-sex couples to wed in England and Wales took effect on March 29 of this year, though legislation protects religious groups including the Church of England and the Roman Catholic Church from facing legal action if they choose not to conduct gay marriages.
In February, the House of Bishops issued guidelines forbidding bishops, clergy and laity in the Church of England from entering into same-sex marriage, stating that although opinions vary, "It would not be appropriate conduct for someone in holy orders to enter into a same-sex marriage, given the need for clergy to model the Church's teaching in their lives".
The Pastoral Guidance on Same-Sex Marriage also notes that: "We are all in agreement that the Christian understanding and doctrine of marriage as a lifelong union between one man and one woman remains unchanged."
Anglican clergyman Canon Jeremy Pemberton has already defied this ruling, however, marrying his partner Laurence in a hotel ceremony earlier this month. In response to Rev Faull's comments he tweeted, "Thank you, Viv!"
Reverend Stephen Sorby, National Rail chaplain and LGBTI ambassador, also expressed his support, although he suggested that the dean's comments may impact her future in the Church.
"Viv is amazing," he tweeted yesterday. "Will be interesting to see what happens now re: any proposed Bishopric as predicted she'd be first. Good on her."
Rev Faull's comments come not long after Archbishop Justin Welby, who has faced criticism for being unclear about the Church's position on same-sex relationships, revealed that he wrestles with questions of human sexuality ""every day, and often in the middle of the night".
He defended his approach to the contentious issue in a live phone-in with LBC radio's James O'Brien.
"We've got to listen to people. We've got to speak to the Anglican community in other countries, and the LGBT community here. We've got to look at the scripture and the theological questions," he argued.
"We have to treat every human with equal dignity."
