The Society of St Pius X has expressed an interest in purchasing St George’s Church in Gorton, Manchester.
One of its bishops, Richard Williamson, provoked anger after saying he did not believe Nazi gas chambers existed. He later apologised.
Although the group distanced itself from his comments, local politicians have objected to the church sale.
The Church Commissioners which manages the Church of England’s historic assets is considering the sale and has asked for feedback by the end of the month.
A report will then be submitted to the Bishop of Manchester, the Rt Rev Nigel McCulloch, who will in turn make his recommendations.
Williamson has not retracted his expressed views on the holocaust, women’s rights, or Mother Teresa.