"Shall we flip a coin?," UK athletics head coach Charles van Commenee was quoted as saying when asked whether the 38-year-old would be fit for her fifth and final Games.
"She has been walking a thin line every day for a decade, nothing has changed," he said. "Paula is always a concern."
Radcliffe suffered a flaring of osteoarthritis in her left foot a few weeks ago when she flew to Munich to see celebrity sports doctor Hans Wilhelm Mueller-Wohlfart.
The Briton has never won an Olympic medal and has been dogged by bad luck at previous Games.
She was forced to drop out of the 2004 Athens marathon through illness and injury. She finished 23rd in Beijing after her preparations were also hampered by injury.
Last April she ended a half marathon in Vienna in tears after a slow time in a head-to-head with Ethiopian Haile Gebrselassie, who had a seven minute 52 second handicap.
"The thing that worries me is that I did not feel myself out there while running," she said afterwards. "The danger is that it affects my confidence."
- Charles van Commenee