The Daily Star says Essien's injury may force Villas-Boas to intensify his search for midfield reinforcements. One name being considered by the new Stamford Bridge chief is Palermo midfielder Pastore.
But Villas-Boas is facing another transfer tug-of-war with Jose Mourinho.
Napoli were also in the running to sign the Argentine but Palermo president Maurizio Zamparini said: "I haven't heard from Napoli president Aurelio De Laurentiis for weeks. Real Madrid and Chelsea are leading the race for his services."