A ballot of first-class county clubs' chairmen and MCC chairman Charles Fry will take place between July 30 and Aug 13.
The winner will need to be endorsed by the ECB's full membership before the final outcome is revealed on Aug 28.
The new man will then take charge from Oct 2007 to March 2009.
Soper, who is currently deputy to Morgan - the man who beat him to the top job in 2002, is regarded as the favourite to emerge victorious this time after losing twice. He also have lost once to Lord MacLaurin in 1997.
He is credited with doubling Surrey's membership during his eight-year spell in charge at The Oval.
In 2001 he was diagnosed with bone cancer and believes he has at least four years to live, although he has been informed that "within that time a vaccine will come out".
"This is my final ambition but this would be only the start because there are so many things I want to do within the game," the 61-year-old told the Guardian newspaper.
Entrepreneur Clarke, 53, is head of the ECB's marketing committee and negotiated the controversial 220m deal which sold rights to televise cricket in England away from terrestrial television to BSkyB in 2005.
He is a firm supporter of women's cricket and the England women's team is based at Somerset's home in Taunton.