He told Spanish radio station Cadena Cope: "I am still in line to recover in the time expected [April 1]. It is not necessary to say that I will not play again this season."
Arsenal v Watford - Premier League match preview
But Wenger has now confirmed the midfielder will miss another month.
The Frenchman said: "Santi Cazorla is running again outside so it should be three to four weeks more training for Santi."
Cazorla should be back in time for Arsenal's final two Premier League fixtures against Manchester City and Aston Villa.
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