He hopes the timetable will give him scope to nurse his family company back to health after recent signs that trading has picked up and the group has stopped ceding market share. "That's a reasonable estimate," Sir Ken said, "but not a forecast."
As if to underline his continuing grip on the business, the 74-year-old Yorkshireman, who has chaired the group since it floated in 1967, admitted that if the problems of running a bigger group persisted, there was a "possibility" he would change his mind. In any event, he will take on the title of life president when he does finally leave, as Lord Kalms did when he retired from Dixons, now DSG International.
Morrisons set itself a firm three-week deadline to appoint a new chief executive yesterday but said an announcement could come within a fortnight. Marc Bolland, Heineken's chief operating officer, and Ian Meakins, who runs Alliance UniChem, are thought to be the preferred candidates. David Wild, who heads Wal-Mart's German business, is also understood to be on the shortlist.
Once the decision has been made, David Jones, the former Next chairman, will retire as Sir Ken's deputy, having completed his quest to overhaul the group's corporate governance.
The City is agog to see what elements of Sir Ken's reign his successor will rip up, but the executive chairman made it clear that the incomer would not have an automatic carte blanche to make radical changes. "I would certainly spend a bit of time with him on it [the new strategy]," Sir Ken said.
Nigel Robertson, one of the four non-executives voted on to the board at yesterday's annual meeting, said: "It would be a mistake to tear up the culture."
After updating shareholders about the business and thanking Bob Stott, who will leave four weeks after the new chief executive joins, Sir Ken cut short attempts to pay tribute to his chairmanship. He let just one of the 300-odd private investors who had flocked to the hotel on the Bradford ring road laud his tenure.
Speaking afterwards, John Wingfield, an ex-Morrisons employee, said: "That's his way. He's very private." Sid Senior, a former Morrisons area manager, said: "At the end of the day the man is an icon of the retailing world."
Sir Ken said the search for his eventual successor would start "fairly immediately" but declined to be drawn on whether he would appoint headhunters. He professed not to know what he would do as life president but added: "Be a nuisance. Does that sound reasonable?" Beyond that, he said he hoped some "hard labour" would help his small family farm to turn a "marginal profit". And since old habits die hard, he predicted he would not stop "polishing produce" as he traipsed round stores. Even competitors. "Voluntary work helping JS [J Sainsbury's]!"
In a trading update, the company said like-for-like sales for the 16 weeks to 21 May had risen by 3.7 per cent excluding fuel, beating forecasts. Total sales excluding fuel rose 5.5 per cent after accounting for the stores it had sold. The group, which this time last year was forced to confess it had no clue about the true state of its finances, said it was comfortable with profit expectations in the market. Shares in Morrisons, which have proved remarkably resilient, closed 5p higher at 194.75p.
The challenge of finding sites and distractions from integrating Safeway meant Morrisons would open only four new stores this year, against its target of eight to 10, Mr Stott said.
Joining in the debate raging on healthy eating, Morrisons said it would follow Tesco's lead in putting "guideline daily amount" labelling on the front of all its packs, starting next month. Its decision is another blow for the Food Standards Agency, which had wanted to see all supermarkets adopt the red, amber and green traffic light guidance used by Sainsbury's.