Essien, who spent eight seasons playing alongside Lampard at Chelsea and won multiple trophies, has warned Lampard that he faces increasing pressure if he fails to meet expectations.
"He was one of the leaders but I didn't really see that he will end up becoming manager," he told talkSPORT.
"But knowing Frank, he's very quiet and calm and he does his thing.
"I'm not surprised he took on that job and at Chelsea he obviously knows the club very well."
He added: "Chelsea's not an easy place to come as a manager or even as a player.
"In his first year he was not allowed to make a lot of signings but he still managed to do well.
"Hopefully they will do even better this season."
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