Shooting's world governing body wants to keep the 2012 event in Woolwich
Moving the Olympic shooting venue from Woolwich to a brownfield site in east London would save more than £10m, says the boss of Barking & Dagenham Council.
A decision on whether to move the event from its proposed site at the Royal Artillery Barracks will be taken at an Olympic board meeting on Thursday.
The south London venue is the preferred option for the Games' organisers, while British Shooting backs Surrey's Bisley.
But Rob Whiteman believes a new option, Barking Riverside, is the "safest bet".
"London 2012 must be about lasting legacy and regeneration," Barking and Dagenham Council's chief executive told BBC Sport.
"We are in the heart of the East End and it would seem odd to me for Barking and Dagenham to not benefit from the Olympics coming to east London.
"By bringing the shooting event here we would be able to create real interest in the Olympics in the borough and create a shooting venue that local people can use after the Games."
It is this issue of a bricks-and-mortar legacy for the sport that has dominated the debate about the shooting venue ever since London won the right to host the Games in 2005.
Plans to stage the competition in Woolwich have infuriated the shooting lobby from the beginning as the proposed venue is a temporary 7,500-seat structure that will be taken down after the Games have finished.
We are a safe bet because a shooting venue at Barking Riverside is more deliverable than the other venues
Barking and Dagenham Council
Using temporary venues was a key aspect of London's original bid as it was intended to keep costs down and reduce the risk of leaving behind "white elephants" - something that has plagued previous Games and caused concern at International Olympic Committee (IOC) headquarters.
But as costs at Woolwich have risen - from an initial quote of £30m to a latest estimate of £42m - the logic of spending so much on a building that will only be used for a month has been increasingly called into question.
This has renewed hope among shooting enthusiasts that Bisley, the spiritual home of British shooting and the venue for the 1908 Olympic competition, will get the nod.
The 3,000-acre site was London 2012's original choice for the shooting competition but lost favour when it became clear it needed a major upgrade and the IOC and international shooting federation had their hearts set on a location closer to the main Olympic hub.
In fact, the "compactness" of the Games was a key bid pledge for London and that is widely believed to be the main black mark against Bisley, as it is 40 miles from the Olympic Park in Stratford, and Dartford in Kent, another potential venue being considered.
Bisley's backers, however, say the competitors can all be accommodated on site and point out that a number of other sports, such as canoeing, rowing and sailing, are being staged away from Stratford. They also claim that improving Bisley's facilities will cost only £28m.
This figure is £2m less than Whiteman's proposal for Barking Riverside but his site is less than five miles from Stratford, with good transport links.
The 350-acre plot, which occupies a 2km strip on the Thames near the Ford car plant in Dagenham, only joined the race to host the shooting when the Olympic Delivery Authority (ODA), the agency responsible for the Games' infrastructure, asked Barking and Dagenham to come up with a fall-back plan last autumn.
Bisley hosted shooting at the 1908 Olympics and 2002 Commonwealths
"Barking Riverside has gathered momentum," said Whiteman. "It started off as a contingency plan but is now a very attractive option because it's cheaper, creates legacy and would be very good for east London.
"We are a safe bet because a shooting venue at Barking Riverside is more deliverable than the other venues.
"The site is already in public ownership, we don't have any planning issues and the background work is paid for. We could start work immediately and be finished by 2010."
Whiteman's proposal is also based on a temporary venue for the competition, but unlike the Woolwich scheme that venue will be relocated and converted into a smaller, permanent facility that will house the area's four shooting clubs.
Despite the buzz growing around his plan, Whiteman admits Woolwich and Bisley remain the frontrunners (and a London 2012 source has confirmed to BBC Sport that Woolwich is still the favourite) but he remains optimistic.
"It's likely to go to one of those venues but there are technical problems in delivery with both of them," he said.
"That is why the ODA asked us to work up a proposal. We've done that and would of course be very happy to hold the event if they decide to give it to Barking Riverside. It's a fantastic site.
"We could step in very quickly if something happened to one of the other two venues and regardless of what is decided on Thursday we will carry on working up the costs and viability of the plan in order to ensure there is certainty we could step in further down the line, if need be."