Produce Investments, which has its head office and one of its three UK packing sites in the Scottish Borders, is expected to pay around £12 million for the business.
The independent Jersey Royal Company employs 500 staff at peak times and produces some 25,000 tonnes of Jersey Royals a year, grown by 20 farmers over 1800 hectares of land.
Jersey Royals are favoured by chefs and known for their distinctive taste, which is created by the soil and growing conditions on the Channel Island.
The potato is understood to be the only fresh fruit or vegetable in the UK to enjoy EU Protected Designation of Origin (PDO) status, owing to the way it is grown, cultivated and harvested.
Champagne, Parma ham and Camembert cheese are among other products which enjoy the status, which provides legal protection against their imitation by other producers.
A spokesman for Produce Investments, which supplies retailers such as Tesco, Sainsbury's and Marks & Spencer, was unable to comment on the Jersey Royal bid as the deal has not been agreed. But he said the company, which has 250 staff in Scotland, has long had a strategy to achieve growth both organically and through acquisitions.
Its most recent deal saw it acquire Rowe Farming, a Cornwall-based grower and supplier of new and salad potatoes, for £12.3m plus shares in October 2012.
The Produce Investments spokesman said: "It would seem to be a very sensible acquisition. It's what they do.
"It [Jersey] is a great brand and I don't think this sort of deal would come as any surprise to the market."
The Jersey Royal Company could not be reached for comment.
The Jersey talks come after Produce Investments, whose operations span seed production, growing, processing, packing and supply, booked what it said had been a strong performance amid poor crop growing conditions in the year to June 29, 2013.
Despite poor weather leading to the "lowest yielding and poorest crop quality since 1976 at 4.5 million tonnes", pre-tax profits rose to £7.6m from £6m, on turnover up to £206m from £153.9m.
The results included a nine-month contribution from Rowe Farming, trading at which was ahead of expectations following a positive response from customers and suppliers.
Analysts said its performance had been better than expected, and signalled their expectation of further growth for the firm in its current financial year.
Shore Capital, which commended the 2012 acquisition of Rowe Farming, pencilled in pre-tax profits of £10.1m for full-year 2014, while Investec upgraded its profit forecast from £9.2m to £10m.
In a statement released to the stock exchange yesterday, Produce Investments said: "The company notes the recent press speculation regarding a potential transaction with the independently-owned Jersey Royal Company and can confirm that the company has entered into heads of terms and has agreed a period of exclusivity in relation to a potential acquisition of The Jersey Royal Company.
"The heads of terms are non-binding and subject to due diligence which is progressing.
"The company will make a further announcement in due course if appropriate."
Shares in Produce Investments closed up 27.5p or 12.79% at 242.5p.