They could have lost him for six matches if Ghana reach the final of the competition.
But sports minister Osei Bonsu Amoah has recommended Ghana's football association accept a deal to have Essien for the first two group games.
Amoah said: "The decision has to be taken by the coaching staff, but I'll recommend the Ghana FA make it."
Chelsea will be without both Essien and Ivory Coast striker Didier Drogba during the African Nations Cup in Egypt next month.
Chelsea's request that Essien commute to and from the tournament in Egypt by private jet was rejected by Ghana.
Under the deal, Essien will miss Chelsea's FA Cup third round tie against Huddersfield, and the Premiership games against Sunderland and Charlton.
Essien will then be available for Ghana's games against Nigeria and Senegal, but miss the final group game against Zimbabwe.
But it remains unclear whether Essien would return to Egypt if Ghana reach the knockout stages of the tournament.