Foodstuffs - which operates New World and Pak'nSave stores - is the New Zealand-owned half of the country's supermarket duopoly, competing against Australian-owned Countdown.
Anderson said Bell had received unsolicited approaches from three potential buyers, whom he declined to name, three years ago.
While multinational food giants such as Nestle and Unilever come to mind as obvious potential bidders, Anderson said a sale to a private equity player was also possible.
"And there's potential international players who aren't in the New Zealand market as well," Anderson said.
State-owned Chinese food firm Bright Food - whose subsidiary Bright Food & Dairy purchased a controlling shareholding in Canterbury dairy processor Synlait in 2010 - has been on a global acquisition hunt in recent years, snapping up majority stakes in Britain's Weetabix and Australia's Manassen Foods.
Anderson would not reveal Bell's potential value, but said Foodstuffs was in no hurry to sell and would hold on to the firm if the price wasn't right.
Bell chief executive Mark Hamilton said the firm's annual revenue was just over $60 million but declined to disclose its profits.
The company was the dominant player in the New Zealand tea market in 2011, commanding a 45 per cent share of the retail trade, according to market research firm Euromonitor.
One market source said it was difficult to estimate Bell's value without knowing its profit.
Bell Tea & Coffee Co
* Head office and factory in Auckland, with another plant in Dunedin.
* Brands include Bell Tea, Twinings, and Gravity coffee.
* Annual sales of about $60 million.
* Around 200 staff.