Milan are said to be realistic about their chances of keeping to Colombia international, especially if they fail to secure Champions League football next season.
According to the claims, Milan will push for Blues target Simone Zaza as soon as Bacca is sold.
Zaza, 24, is tipped to leave Juventus this summer after failing to lock down a regular slot in manager Massimiliano Allegri’s first XI.
But Milan could match any offer Chelsea make with the funds raised by Bacca’s sale.
Tuttosport claim the San Siro club could earn £28m from the Arsenal transfer, although the Gunners themselves are facing competition from Bayern Munich for 29-year-old Bacca.