Langholm Capital, a private equity firm, has owned the Herefordshire-based business for the last five years after buying it from potato farmer William Chase in a £40 million deal.
According to the Sunday Times, Tyrrells is likely to draw interest from American food giant Kellogg's, the Japanese snacks firm Calbee and Tangerine, the Blackpool-based confectionery company that owns Butterkist popcorn.
Other potential bidders could include Germany's Intersnack, which bought KP Snacks last year.
Under Langholm, which is backed by the household goods firm Unilever and also owns Dorset Cereals, the company has enjoyed success in expanding its operations to new overseas markets, including the US and Canada.
Mr Chase turned to making crisps when his margins as a potato farmer were wiped out by the supermarkets. The crisps gain their flavour through the use of special potato varieties such as Lady Rosetta.
He claimed a victory with Tesco in 2006 when he found the group was stocking Tyrrells Potato Chips at reduced prices, forcing the chain to take the crisps off its shelves and pledge to boost links with local suppliers. The business was founded in 2002.