'He's had a date on his calendar for two years,' said Norman's spokesman, John Story. 'It's a bad situation but we're still hopeful Greg might be able to play the Open.'
Norman's only remaining chance is to be granted a 'special exemption' by the USGA.
Norman is 55th in the latest world golf rankings. Only the top-50 following this week's Kemper Insurance Open automatically qualify. Norman is not in the field.
The 46-year-old Norman has missed the cut in his last three U.S. Open starts, his last two PGA Championships and last month's Masters.
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