Sky Sport Italia are suggesting Alessandro Matri could complete his proposed move from Juventus to Milan within the next 48 hours.
The Diavolo confirmed on Wednesday evening that they are looking for a striker after qualifying for the group stages of the Champions League.
Matri, who is available for transfer, has also been linked with the likes of Napoli and Roma this summer.
The Italian international will cost the Diavolo €12m, although the two clubs are still discussing payment terms.
Juve, it is being claimed, will either get an initial €11m plus a further €1m in bonuses or €10m with a later additional €2m.
Milan boss Massimiliano Allegri has worked with the 29-year-old in the past when they were both at Cagliari.
Matri, signed by Juve in January 2011, was netted by the Diavolo youth system in 1996. He remained on Milan’s books until his 2007 switch to Sardinia.