I believe the Essien to Milan was just a rumor Jack. Denied ever since by everyone in Milan.
Actually, they denied that Pirlo and Seedorf will leave. Berlusconi said that Pirlo, Pato and Seedorf are untouchable, Pirlo said that he's certainly staying in Milan, Galliani said that no more stars will be sold if Kaka leaves.
Maybe Milan will try to buy Essien (although absolutely no indications exist for that, except for that newspaper rumor about a swap Essien-Pirlo+Seedorf) but i doubt that they will buy players for the midfield (apart from an AMC maybe). They have Pirlo, Gattuso, Ambrosini, Flamini and Beckham will be back in September.
At least i hope so.