All the potential qualifiers have decided to play in the Women's World Matchplay event which clashes with the Open qualifying tournaments.
Teenager Michelle Wie could still qualify to play at Hoylake.
However to do so she would have to be the highest non-exempt finisher at the previous week's John Deere Classic.
Wie has so far failed to make the cut in any of the men's PGA Tour events in which she has played.
The R&A's Peter Dawson said: "The deadline for entries for qualifying is June 1 but as yet, no women players have entered.
Watch this space, I guess...
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