Market analyst Nielsen said volume sales of the cereal dropped 18.3 per cent for the year ending in October, while value sales slumped 6.6 per cent to £29 million.
Earlier this month shadow health secretary Andy Burnham said ministers should consider banning cereals like Frosties and Sugar Puffs as part of the battle against Britain's growing obesity crisis.
The Grocer claimed that a ban on the advertising of foods high in fat, sugar and salt on children's television, introduced in 2007, had harmed sales of a number of cereals including Frosties.
In an article published on Saturday, the magazine said: "Tony the Tiger has not been feeling too grrreat of late. Tony is facing an uncertain future as Kellogg's weighs up options – including cutting sugar content – for the ailing Frosties brand."
Kellogg's has not spent a penny on traditional advertising for Frosties since 2010 when it spent £1.1 million, it was reported.
Pete Harrison, Kellogg's marketing director, said: "Because of concerns voiced in public affairs we have not supported Frosties as much as we have historically. But it is not as if it is gone altogether.
"We did introduce a reduced sugar alternative to Frosties a few years ago but that was not successful. It's got to be what people want."
Last week Kellogg's announced the launch of three new cereals, all of which are low in sugar to meet criteria for advertising on daytime television.