According to Italian sports newspaper Gazzetta dello Sport, Milan representatives have travelled to Barranquilla, Colombia, where Bacca is currently on holiday, to oversee a medical.
Sevilla confirmed on Wednesday that AC Milan were prepared to pay Bacca’s ??21million buy-out clause to acquire the South American this summer.
Sevilla sporting director Monchi expects Bacca’s future to be decided by the end of this week.
Monchi said on Sevilla’s official website: “Carlos Bacca’s future will be resolved in the next few days.”
The Colombia international, who has three years left on his contract with Sevilla, already agreed personal terms with Milan last week.
Bacca, 28, joined Sevilla from Club Brugge in 2013 and has scored 34 goals in 71 appearances for the Andalusian outfit.
Sevilla want to keep Bacca, who was prolific in the Primera Division last season, scoring 20 goals in 37 appearances to help Sevilla finish fifth.
The South American also scored seven goals in the Europa League, including two in last month’s final that saw Sevilla beat Dnipro 3-2 to win the competition for a record fourth time.
Unlike Milan, who will not feature in Europe next season after a 10th-place finish in Serie A, Sevilla will play in the Champions League next term.
Bacca recently competed with his national team at the Copa America in Chile.