The agency has yet to publish its draft strategy on the matter, and most food industry associations claim they have no idea what the FSA will come up with.
But meat industry bosses have been told verbally by officials that they will be expected to cut fat levels in products such as pork pies and sausages.
The agency is also applying pressure on the dairy industry to cut fat levels in milk, cheese and butter - although trade body Dairy UK has warned such levels are dictated by EU law.
In one case, the FSA has suggested the fat content of semi-skimmed milk be cut from 1.5% to 1%, but under existing rules, a 1% fat milk cannot be marketed as milk.
The FSA has also suggested that low-fat variants of dairy products be repositioned as the standard SKUs.
The news emerged in the week the government published a high-profile report that indicates nearly a quarter of adults are obese and the UK is the fattest nation in Europe.
The damning data means there is likely to be a wrangle between the FSA and industry, similar to the one seen last year for salt, as manufacturers and scientists seek to agree on what cuts are feasible. The FSA, which wants to reduce the amount of energy people get from fat and sugar, wrote to trade associations in June asking for details of what cuts in fat and sugar content manufacturers had already made, and what they believed possible.
The agency said it would use this information - much of which it is yet to receive, The Grocer understands - to inform its approach.
Publicly, the FSA has not ruled out reformulation, nor has it confirmed it will demand this from the industry - a stance re-affirmed this week to The Grocer. A spokeswoman said: "At this stage all options for the draft strategy, including potential reformulations, are open."
Ed Komorowski, technical director at Dairy UK, said the FSA's preference for reformulation was at odds with its traffic light labelling. "On the one hand it is in favour of helping consumers make choices themselves, but on the other it appears to have a lack of trust in consumers' judgement so it wants to restrict their choice."
Maurice McCartney, director of the British Meat Processors Association, warned there were cost and practical implications to reducing fat in meat lines.
"Lean meat is more expensive than fatty meat, and you have to consider retailer pricing strategies. You also have to ask what would happen to the excess fat. Does it go down the drain or end up somewhere else in the food chain?"
Alison Ward, director of communications at the Biscuit, Cake, Chocolate and Confectionery Association, said she believed the FSA might not demand reformulation from all suppliers.
"I think the agency recognises fat and sugar are more complex than salt and may treat different sectors in different ways."