The ex-Udinese midfielder has no doubt that the Ghana international will prove himself at San Siro, but was quick to add that it requires patience.
The 31-year-old left Chelsea to join the struggling Italian side this winter, but his addition has done little to revive the fortunes of the Rossoneri and Essien has struggled to make his mark on the first team.
Essien has so far made five Serie A appearances and two Champions League outings since joining Clarence Seedorf’s men and has yet to score, but his former Ghana teammate believes he will require some time to adapt as he is lacking game-time.
"I have no doubt that Essien will find his rhythm," Appiah told Goal. "He is the type who never gives up and very soon Michael will return to his previous form.
"When players get injured it takes time, and in Michael’s case he has gone under the knife several times so people need to understand his situation. The fans must exercise patience. Essien will bounce back and I believe it will be soon."
Essien is expected to return to Stamford Bridge, where his deal runs out in June 2015, in the summer once his loan spell at San Siro expires.