Alternative plans for a Concorde museum in Bristol have been submitted to British Airways.
The Save Concorde Group (SCG) said it met the firm on Tuesday to present its plan which would cost £1.5m.
Another bid by the Concorde Trust for £2.9m of lottery funding towards a £9m museum has been rejected.
The jet was on display in Filton until late 2010 but was closed by Airbus, which has been loaned the jet, so the firm could carry out maintenance.
The firm has spent £1.4m repairing Concorde with water leaks a particular problem because it has been left on an open runway since 2003.
Ben Lord from SCG said: "It is vital that not only do we preserve Concorde, but educate our future generations what Concorde symbolises."
Mr Lord added his group has become "increasingly concerned" with the Concorde Trust and how they had handled the proposed move to a new museum.
"Following the controversial closure of the temporary museum, it was revealed that the trust were seeking to develop a £9m heritage centre.
"In our opinion [it] was incredibly over exaggerated in terms of cost, and would take an unreasonable amount of time to become open."
A spokesman for the Concorde Trust said it was important that all interested parties worked together to make the Concorde museum a reality.
"The Concorde Trust is happy to work with all stakeholders and to consider any ideas and plans."
Not as glossy
The spokesman added that plans must be financially viable and help to conserve the region's aviation heritage.
Mr Lord from SCG said the discussions with BA "went very very well" and had taken the plans away for discussion with Airbus who are looking after the jet at its Filton base.
He said his group's plans were "not quite as glossy" as that of Concorde Trust and would see the jet brought under a hangar at a site earmarked for the museum at Cribbs Causeway.
He said £840,000 of funding from Airbus, with £300,000 already saved for the museum would be supplemented with funding from commercial sources.
The plane - called Concorde 216 or Alpha Foxtrot - was the last of the fleet to fly when Concorde was withdrawn from service by British Airways in 2003 due to increased running costs.
The Concorde Trust plans for the museum at Cribbs Causeway were first submitted in 2007 but building work has never started because of a lack of funding.
The museum was given a £840,000 cash boost by Airbus last week but has almost £8m still to raise.
The jet has been at Filton since 2003 and was closed to the public in October 2010 for maintenance.
Filton Airfield, where the jet is based, is to close from the end of 2012, meaning a new home will soon have to be found for the jet.