The pair were pictured sitting together in VIP box at the Stamford bridge cheering their old club.
Chelsea failed to score in a match at Stamford Bridge for the first time this season as Everton held on for a 0-0 draw in the Premier League on Sunday.
Chelsea dropped to third place and two points behind Liverpool after 12 games, but remained unbeaten.
Essien is currently without a club after parting ways with Indonesian outfit Persib Bandung.
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