Running costs and dwindling public funding are said to be causing the problems.
Bishop of Stepney Rt Rev Adrian Newman is overseeing a group looking at ways to solve the issues.
Speaking to the Guardian, he said: "My finger-in-the-wind estimate is that perhaps half of cathedrals are facing some significant financial challenges, although pretty much all of them are planning on how they're going to get through that.
"Although it seems unimaginable, it is possible to imagine a situation where an individual cathedral could get into a situation so desperate that there is no obvious solution."
Charging money for entry is one idea being explored.
It's reported just nine out of 42 cathedrals currently have an entry fee.
Westminster Abbey charged £20 to visitors.
The Cathedrals Working Group is expected to report its findings and suggestions in December.