The plan is being offered by the charity's outgoing chief executive, Terry Prendergast, as a way to continue what are seen by the Church as conflicting roles.
Marriage Care has its roots in the Catholic Church but in recent years has broadened its client base and developed into Britain's second-biggest provider of relationship counselling.
Mr Prendergast says the charity has counselled both heterosexual and gay couples and it offers preparation for "a trickle" of same-sex couples entering civil partnerships.
The civil partnership cases have strained the charity's relationship with the Catholic Church.
In September, Marriage Care's president, Archbishop Vincent Nichols of Westminster, warned the charity that it must conform to Catholic teaching.