Nigel Farage, the UKIP MEP for the South East, said: "I think people would like him to stand. It would be a tremendously good idea."
Many people believe that the former Labour MP is the only candidate capable of mounting a campaign that can challenge Labour.
Those close to Roger Knapman, the UKIP leader, think otherwise. One party member said: "Keeping Kilroy down has become more important than getting an MP." The winning candidate is likely to be a relatively unknown local activist.
A UKIP spokesman insisted that Mr Kilroy-Silk could still apply for the seat although he put the chance of that happening at just 50-50.
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