The Italian club reached an agreement on Tuesday night over the transfer of Krzysztof Piatek, who is also set to have his medical with the Serie A side.
Milan will pay Genoa £31m (€35m) plus bonuses, according to Sky in Italy.
Piatek’s arrival at the San Siro means Higuain’s loan to Chelsea can be completed with Maurizio Sarri’s club trying to register him in time for Thursday’s Carabao Cup semi-final against Tottenham.
Higuain was left out of Milan’s team for their 2-0 win over Genoa in Serie A on Monday, with manager Gennaro Gattuso admitting the striker had told him he wants a move to Chelsea.
The 31-year-old is currently on loan at Milan from Juventus and has scored six goals this season.
Milan and Chelsea have already agreed terms on a loan deal until June with an obligation to renew it for another 12 months upon certain conditions.
The deal will allow Higuain to reunite with Sarri, under whom he equalled the Serie A record for goals scored in a season, with 36 for Napoli in 2015/16.