The last two Catholic high schools in inner-city Salford, Manchester, face closure because of falling rolls.
Pope John Paul II school in Charlestown and Our Lady of Mount Carmel in Weaste now have under 600 pupils between them, with numbers likely to fall further.
Local education authority and diocesan leaders say the problem reflects falling numbers of families in the inner city, and parents exercising their choice of schools.
They say 300 children living near the two schools are sent instead to other Catholic schools further away.
According to council and church leaders, an earlier consultation among parents showed little support for a planned new school on one of the sites, although parents claim they were not told the full facts.
Now in a second attempt to gauge opinion, more than 700 parents have been sent questionnaires to ask if they would support opening a new school. Given enough support, the decision by Salford's education committee not to open a new school could be reversed.
Principal education adviser Harry Pickles said: "We were concerned that because of their size the two schools could no longer offer good-quality education. We would dearly love to have a Catholic high school in the city but it would have to be viable."