The game's governing body have been working closely with joint administrator Brendan Guilfoyle as he looks to find a buyer for the cash-strapped club whose future has been under some question for most of the season.
One of the bids is from Super League Europe Ltd and three other bids have also been tabled, with all parties required to submit business plans by next Tuesday.
The RFL have refused to confirm who the interest is from, although it is believed Bradford City co-chairman Julian Rhodes is behind one of the groups, and chief operating officer Ralph Rimmer is positive about the club's future in light of the fresh advances .
In the absence of an official club website, a statement from Rimmer released on Bradford's Facebook page read: "We had constructive meetings with all the consortia that have submitted proposals to the administrator and we're optimistic about the future of Bradford Bulls.
"There are now four confirmed bids for the Bulls and each consortium has been asked to submit business plans to us by Tuesday, August 21. Due to the sensitive nature of the current discussions we are unable to confirm who the bids are from at present."
Rimmer also believes bids have been tabled in light of the offer made by Super League Europe, adding: "It does appear that this renewed interest has come as a direct consequence of the offer from Super League Europe Ltd, which remains on the table.
"We understand the frustration regarding the ongoing process but it is vital that due diligence is carried out on all the bids and that ultimately the right owners are found for the good of the club and the sport as a whole."
Guilfoyle met with the RFL to discuss the bids yesterday and is happy that all interested parties have the necessary funds to satisfy the governing body's criteria for a buyout. "We are pleased to be working collaboratively with the RFL to agree on a purchaser and sell the club," he said.
"We now have all the ingredients that the RFL has requested and funds proven from three bidders plus the Super League Europe Ltd offer. The RFL will consider the bidders' business plans which are to be received by the Tuesday deadline, and all concerned do understand the need to bring this to a swift conclusion."