Well there will be a supermarket unit in the basement of the new PricewaterhouseCoopers building (7 More London Riverside) currently under construction so it's plausible, though I don't think the space is particularly big by Waitrose's standards.
I know they have a few modestly sized city centre stores these days, though.
( You're not just being mischievous, though, are you? )
When I spoke to Waitrose some time ago about a store in SE1, they said that they had no plans for one and to visit the branch at St Katherine's Dock, just across the river. Perhaps they have changed their minds?
If they did move into More London, we'd probably be one of the best served areas of London for groceries: Waitrose, Sainsburys, Tesco, Asda, Borough Market all within walking distance.
Unless I've missed a spate of supermarket openings, I don't think that's right. There is no Asda within walking distance of More London. Sainsbury's (Bororugh High Street), Waitrose (St Katherine's Docks) and Tesco on Great Tower Street are all a good 20 minutes walk. That's a 45 minute round trip for a pint of milk.
Great local shops and M&S of course. But no major supermarkets.
The rumour might perchance have started with those involved in trying to let unoccupied (or more probably looking to assign soon to be under-occupied) office space in More London and nearby. [/cynicism]