"Our predictions make it unlikely England could actually make a profit out of hosting a World Cup in 2015," said RFU chief executive Francis Baron.
"It puts an absolutely massive financial risk on the bidding union. The RFU Board would have to consider very carefully whether or not it would be prudent to risk the game's money in bidding in the knowledge that almost certainly we would make a substantial loss.
"I have explained to the IRB that England is the largest rugby-playing country with access to some of the biggest stadia in the world like Twickenham and Wembley. But at the moment we just can't make the numbers work because of the scale of the financial guarantee that is required."
Baron's comments come after Australian Rugby Union chief John O'Neil expressed similar concerns surrounding the International Rugby Board's demand for a guaranteed sum of profits from the event.
The cost of hosting the 2015 World Cup is believed to be in the region of £100 million, with the finances needed to hold the following tournament in 2019 expected to rise to £120 million.