It follows a refusal by ministers to underwrite the Ebbw Vale project.
The Heads of The Valleys Development Company said it has put forward two alternative options with revised commercial terms for its backers Aviva and two local councils.
Ministers were asked to provide a 100% guarantee but rejected it as too risky.
The Heads of The Valleys Development Company, behind the project, said it had put forward two alternative options with revised commercial terms.
"These alternative arrangements will reflect a more balanced financial support package for both the public and private investment parties," said chief executive Michael Carrick, who added private financiers would take a share of the risk.
So a guarantee by Welsh Government could be less than 80% of the project compared to the 100% that was rejected on Wednesday.
He said no public money would be tied up underwriting the circuit while it was being built.
In the worst scenario afterwards, the Welsh Government would own the land and the assets.
Mr Carrick said the deal was already there with leases, construction contracts and guarantee agreements "ready to go".
"This is a small nuance on an existing deal that we can look to put in place relatively quickly," he told BBC Wales.
"There are challenges around internal and government approvals to a structure like this - it's not something we can do imminently. We're not looking months but four, five or six weeks to be able to do this."
The race track and related developments aims to eventually create 6,000 jobs.
On Wednesday, Economy Minister Edwina Hart said there was a "significant question around the viability of the project" and an "unacceptable risk" to the government underwriting the entire project.
Mrs Hart said she had "reluctantly come to the conclusion" not to proceed with the guarantee after legal advice.
The Welsh Government has already in effect spent around £9m in supporting the development, which Mrs Hart said had not been wasted, and included feasibility studies.
The minister said she "did not want to close the door to it all, just close the door on this stage of it".
The stumbling block came when ministers were asked to underwrite the whole of the private sector investment.
First Minister Carwyn Jones said the problem emerged in the "last few days" and they could not take on board an enormous risk to taxpayers.
"It would mean effectively a bill of £100 for every man, woman and child if things went wrong," he told BBC Wales.
"Any rational government is going to ensure there is not an unacceptable risk to the people of Wales."
All sides seem to still want to make this happen, as part of regenerating the area.
Earlier in the day, Circuit of Wales said it would continue working with Welsh Government, local authorities and Aviva investors to take the project forward in a way that is acceptable to all sides.
Blaenau Gwent Nick Smith MP said there had been major difficulties since  the project was first unveiled past four and a half years ago but he still hoped it had a future.
"The Welsh Government was clear about what the difficulties were but I studied (its) letter carefully and it said it was open to a different way forward.
"We need some imagination, we need some ambition and that different way forward given the efforts so far locally, by the council, by Welsh Government and the developers."
Meanwhile, TVR said Ebbw Vale was still the "location of choice" for the sports car firm, after it announced its intention to create 150 jobs in the town's enterprise zone.
The team behind the £357m Circuit of Wales has said it hopes to have a new deal agreed to allow the project to go ahead within six to eight weeks.