If selected, 42-year-old Mr Norman will almost certainly become the first heavyweight business recruit to the ranks of Conservative MPs in 30 years.
The last was John Davies, a former managing director of BP and chairman of the Confederation of British Industry, who succeeded Sir Walter Bromley- Davenport at Knutsford in Cheshire in the 1966 general election.
Mr Norman is up against stiff competition to succeed the retiring Northern Ireland Secretary, Sir Patrick Mayhew, who holds a 21,000 majority in the Kent spa town.
Alan Clark, the philandering former minister, is in the race, along with several MPs - deputy Commons' speaker Dame Janet Fookes and Finchley's Hartley Booth - who have lost their seats due to boundary changes.
But even rivals not sporting "It Asda to be Archie" badges believe he has the credentials and ambition to go all the way. "I don't think there's anyone he can't beat. Locals will be very intrigued. By the standards of other people, his CV is hard to beat," said one unsuccessful candidate, who failed to make it through 200 applicants for the first interview round.
Cambridge and Harvard educated "Stormin' Norman", Asda's chief executive since 1991, has been a Tory-approved candidate for 15 years and turned the Leeds-based supermarket chain around from losses of pounds 365m in 1992 to a pounds 304m profit last year. Speculation about a seriously political future was prompted by his decision three weeks ago to go part-time as chairman from December.
His Who's Who entry lists fishing, skiing and tennis as hobbies. It might also include bashing the net book agreement, price-fixing in drugs, standing up for British beef and other, often gimmicky campaigns by Asda in the past year.
Mr Norman was unavailable for comment this weekend, and the supermarket chain, plus the Tunbridge Wells local party, were tight-lipped on his candidacy. An Asda spokesman denied speculation, however, that the chain's policies were part of Mr Norman's CV-building.Reuse content