According to the Daily Telegraph, Most Rev Justin Welby made the comments after Guildford Cathedral (inside, above) was denied planning permission to begin the building of 134 apartments on surplus land it owns, in the hope of raising £10 million.
The newspaper reports the cathedral, which welcomes around 90,000 people a year, is losing £100,000 a year.
Guildford Cathedral is one of Britain's newer ones, having been completed in 1961.
In a letter to Guildford Council before their decision to reject the cathedral's development plans, the Archbishop said: "It is sometimes said that cathedrals are the Church of England's equivalent of the big banks - 'too big to fail' - and that the very serious financial straits that are one of the motivating factors for Guildford pursuing this application are not so serious because the central church would 'rescue' them before total collapse.
"This is not the case."
Dean of Guildford, Very Rev Dianna Gwilliams, told the paper: "We believe the development proposal is the only way to raise the necessary endowment."
A Guildford Cathedral spokesman said: "Clearly we are disappointed by the decision. We will carefully consider the reasons for refusal before deciding the next steps."
