Italy's summer transfer window closes on Friday and Sportmediaset says Lazio president Claudio Lotito is prepared to sell before the deadline falls.
Lotito will sell for €120m cash - and Milan are the closest to meeting the president's valuation.
Milan have already offered €40m for a 12-month loan with the obligatory permanent option for €80m next June. However, Lotito turned it down.
But he is now willing to relent if Milan adjust their proposal over the next 48 hours.