The company is denying the story vigorously, but the rumours that Sir Terry is coming to the end of his time at Cheshunt refuse to go away.
As Sir Alex Ferguson is probably thinking right now, if you're one of the greats of your profession, it's better to step down while at the top of your game than hang around and fall victim to the inevitable downturn in your fortunes.
Sir Terry has presided over a period of phenomenal growth at Tesco, overseeing the hugely successful diversification into non-food and the expansion of the business overseas. But from here on times are likely to get tougher. There is a groundswell of opinion among influential groups - although, it must be stressed, not shoppers - that Tesco has become too powerful.
There is a good chance that the regulatory environment will get significantly tougher and, having had an easy ride against weakened competitors in the UK, Sainsbury's is resurgent, Asda is under strong new management and Morrisons is getting over the hiatus caused by the Safeway takeover.
That is not to say that any of these represent a threat to Tesco's supremacy, but there are big challenges ahead. If you've achieved as much as Sir Terry, maybe it's natural to want to take on a bigger challenge - and there's no bigger challenge than that of leading the bureaucratic nightmare that is the NHS.
It may not be today, tomorrow, or next year, but don't be surprised if the rumours do become reality before too long.