Greencore confirmed on 25 October that an unidentified party had made an approach that could lead to an offer.
The company, which makes sandwiches for Tesco, is one of the supermarket giant’s biggest suppliers. It also makes ready meals for Weight Watchers, and Bisto gravy.
CD & R, which appointed Sir Terry as a senior adviser in February, has experience in the sector after acquiring ready-meal maker US Foods in 2007.
Any deal would cap a tumultuous year for the Irish firm.
Poultry giant 2 Sisters Food Group scuppered Greencore’s merger with Northern Foods in March, by snapping up the company for £342m.
The Irish company then diverted its attention to British sandwich maker Uniq, which it agreed to purchase for £113m in July.
The Office of Fair Trading reported that the tie-up would give the company between 30 and 40 per cent of the British sandwich market.
Rumours over the identity of this month’s bidder had even touched on 2 Sisters, although analysts had also suggested a management buyout.
Fierce competition in the prepared food sector is seen to be driving consolidation.