Parents from St Joseph's Primary, Milngavie, enlisted the support of church bosses in an attempt to save the school.
The school, which has 130 pupils, faces a merger with St Andrew's Primary, in neighbouring Bearsden.
A spokesman for the Archdiocese Of Glasgow said: "The issue of a shared campus is one that has not been formally proposed by the council.
"But we have agreed to shared campuses in other places as a last resort to preserve Catholic education in an area, under conditions that guarantee and protect the Catholic identity of the Catholic school in the shared campus.
"The Archdiocese is willing to engage positively with East Dunbartonshire Council on any proposal that retains a Catholic school in Milngavie."
The council is consulting on the proposals to close and merge St Joseph's.
The school's parent council published a paper in August with proposals for a shared campus, library and sports facility.
Parents of children at St Joseph's and supporters held a march in Milngavie on Saturday in protest at the closure decision.
Laureen McIntyre, chairwoman of the Parent Council, said: "We welcome the Church's support. This statement is a game changer.
"It is now clear East Dunbartonshire Council can take forward proposals for a shared campus or a community hub in Milngavie and the Church will support them.
"This is not a new idea. Every other local authority in Scotland has shown that combining services on a single site can produce savings and deliver benefits to the whole community across the generations.
"A shared campus or a community hub would bring with it the opportunity to develop new sports facilities, a baby clinic or even a new library on a single site."
Gordon Currie, the council's head of education, said: "We welcome the input from the Archdiocese. This will be considered within the scope of the consultation process."