Holmes is seen as one of the rising stars at Tesco and has successfully driven its convenience division, aggressively expanding the Tesco Express format.
Morrisons hopes to announce a replacement for long-serving chief executive Bob Stott by its AGM on May 25. Sir Ken has been keen to hand the role to an internal candidate, but pressure from Morrisons' non-execs means it is likely an external candidate will be named.
Alongside Holmes, other names linked to the job include Halfords chief executive Ian McLeod, WHSmith boss Kate Swann and Asda George Global head Angela Spindler.
One industry source who knows Holmes said: 'It would be quite a big step up, but look at Justin King. He went from running a division of M&S to the top job at Sainsbury's. Holmes is certainly very capable.'
Holmes' move would be a blow to Tesco, which has recent-ly lost other top management figures. Colin Smith defected to Somerfield to become trading and marketing director, and Stuart Machin joined Asda as central operations boss.
Holmes became chief executive of Tesco's convenience division in 2004 after the T&S and Adminstore acquisitions. Previously he held store and finance roles at Tesco.
Holmes, Tesco, Morrisons and headhunter Egon Zehnder, which is carrying out the search, would not comment.
Morrisons last week unveiled a loss of£312.9 million for the year to January 29 as a result of Safeway integration costs.
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