The Poland striker has scored 13 times in 19 Serie A games for Genoa this term and is set to replace Chelsea-bound El Pipita at Milan.
Krzysztof Piatek arrived at AC Milan's medical centre ahead of a proposed move from Genoa on Wednesday as Chelsea target Gonzalo Higuaín headed to London.
It looks like being a case of one-in, one-out for Milan, with Higuaín photographed at Milan Linate airport by Italian journalist Michael Cuomo
Chelsea will need to be quick if they are to conclude a loan deal with Juventus in time for the Argentina striker to feature against Tottenham in Thursday's EFL Cup semi-final second leg.
The transfer would need to be registered by 12:00 GMT in order for Higuaín to help his old Napoli boss Maurizio Sarri overturn a 1-0 deficit at Stamford Bridge.
Higuaín joined Milan on a temporary basis at the start of this season following Cristiano Ronaldo's switch to Juventus but has largely disappointed with six goals in 15 Serie A appearances.
Head coach Gennaro Gattuso left him out of the 2-0 win over Genoa, stating the prospect of a move to Chelsea had affected the player's focus, and Milan have turned to their most recent opponents for an instant replacement.
Piatek has made a stunning impact since joining Genoa from Cracovia in June, the 23-year-old Poland international scoring 13 times in Serie A this season.
Higuaín's arrival at Chelsea is expected to herald the departure of out-of-favour Spain forward Álvaro Morata, with Atlético Madrid appearing his most likely destination.