The standard, which was launched in 2007, was axed less than two years later after failing to achieve sufficient buy-in from the trade.
However, the British Standards Institute (BSI) recently announced plans to take it on and develop it.
But Sainsbury would not endorse it unless changes were made, said chemistry manager John Figgins. "It probably needs several large companies, either retailers or food manufacturers, to get behind it if it is to work in its current form.
"However, at the time of launch and in several meetings prior to the launch, Sainsbury indicated that it did not think the standard was pitched at the correct level. It is too stringent for routine product and not stringent enough for 'free-from' products. Unless the standard is updated, we would still have these concerns."
Emma West, operations manager at food safety assurance specialist SAI Global, said she also doubted it would succeed unless a supermarket mandated that suppliers adhere to it. She added: "It needs a retailer to drive it, pick it up and run with it."
However, Anaphylaxis Campaign chairman Tony Hines said he was confident that the BSI would not have taken the standard on unless it was convinced that there would be take-up. One industry source added: "My instinct is that at least one of the major retailers must be warming to it, otherwise, I can't see why the BSI would have taken it on."