Bedford, one of Radcliffe's greatest admirers after her two starring shows in his race, said: "If I was to advise her, I'd say that she shouldn't do the 10,000."
Yet he said he believed she had even faster times in her in the marathon and that he would not be surprised if she tried again in four years' time in Beijing.
"She is still the best distance runner we have ever seen. If you look across the board at all the results it is still easy to support that view.
"We haven't had any conversations yet about the London Marathon in 2005 because we wouldn't want to distract from what she is doing at the moment. She'd be welcome back next spring because she is still the greatest attraction in British athletics. I don't think for a moment that what happened here has affected her popularity."