Ivorian Drogba and Ghana international Essien have won numerous accolades with the Blues, although Drogba is now plying his trade with Galatasaray in Turkey.
"I have a lot of respect for Essien because playing for one of the biggest clubs in the world is not easy," he told BBC Sport "I know that I've a long way to go to get anywhere close to what he's done. Hopefully, one day I'll be mentioned in the same breadth as Essien and Didier Drogba."
Upon his arrival from Porto last week, the 21-year-old was immediately loaned out to Chelsea's feeder club Vitesse Arnhem, where he has expressed his determination to make an impression.
"I'm happy because as a player you always want to be playing to stay in good shape. When Chelsea came for me, I saw a good opportunity to work with a massive club and a great coach. I know I have to prove myself at Vitesse first and I'm determined to do just that," the winger added.
Atsu has signed a five-year contract with the West Londoners.