With the January transfer window now open, speculation is mounting over a potential loan move for the Chelsea man.
Essien has made just two Premier League starts for the Blues this term, adding weight to Milan's chances of securing the suggested six-month deal for the player.
However, Galliani insists the Rossoneri are yet to open talks with Essien or Chelsea over a potential switch, but admits if a midfielder did come in they would be in contention for Champions League action.
"In these days there are a lot of contracts, but there is not a negotiation open with Essien," Galliani stated at a press conference on Friday.
"AC Milan's appeal is very strong and there are many agents offering their players.
"But it is not yet certain that we'll take another midfielder, but having Muntari and Montolivo banned in the Champions League (against Atletico Madrid) it is clear that if a new player will come he should be able to play in the Champions League."
Although Galliani remains coy on a move for Essien, the AC Milan CEO admits a striker is available to leave, taking into account the abundance of attacking options at the San Siro.
"We have nine attackers, even with [Alessandro] Matri away, there are too many," he added.
"It is possible that one of them can leave."