The bet, which the punter tried to place with Irish firm Paddy Power, was one of a number placed on the hotly-contested race to replace Cardinal Cormac Murphy O'Connor, who is expected to retire at the end of this year.
The £40, 000 (€50,000) bet on Monsignor James Curry, who is the parish priest at Our Lady of Victories in Kensington London, took the bookmakers by surprise as he had not been in the running at all until that point.
A spokesperson for Paddy Power said that the bet had been turned down because of the liability it would have placed on the firm.
He said: 'These sorts of bets are of the kind like betting on Big Brother or the Christmas No. 1 where the average stake size is more like £10 - £20 and we can balance our liability.'
Despite this, Mgr Curry can now be backed at 40-1 with the firm.
The favourite to replace the cardinal the Most Rev Vincent Nichols, the Archbishop of Birmingham, who can be backed at 13-8.
Other figures being tipped by senior Roman Catholics include Father Timothy Radcliffe at 6-1and the liberal Bishop of Leeds, Rt Rev Arthur Roche at 12-1.
'We don't take that kind of money on a novelty bet like this,' the Paddy Power spokesperson said.
'When it comes to bookmaking it's all about balancing your liability.
'A bet of that size would have completely skewed our liability and if he had won, we would have lost our shirt on it.'
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(Source: DMO)