Reports suggest that Sir Ken will finalise his plans to retire within the next few weeks.
He is then expected to announce a public timetable for his departure at the retailer's annual general meeting later this month.
The reports follow rumours in the City last week that Sir Ken had stepped down as chairman.
The speculation caused Morrisons' shares to rise, but they fell after the retailer immediately denied the rumours.
Sir Ken has worked at Morrisons since 1952 and was chairman and managing director of the retailer from 1956 to 1997.
However, his position at Morrisons has come under increasing pressure following the retailer's acquisition of Safeway in 2004 and five profit warnings within two years.