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That’s according to Tutto Mercato Web, who claim free agent Zlatan Ibrahimovic is also on the Italian giants’ striker shortlist.

Costa, 28, revealed in June that Antonio Conte had told him by text that he’s free to leave Chelsea this summer.

And since then a return to his adoptive homeland of Spain with former club Atletico Madrid has been heavily touted.

Costa’s agent Jorge Mendes is thought to be pushing his client towards Serie A rather than La Liga though.

(Image: GETTY)

It seems Milan have their heart set on taking Costa to the San Siro before the transfer window closes.

Tutto Mercato Web claim the Brazil-born ace is Vincenzo Montella’s No.1 target.

And they reckon Milan want to take him on a year-long loan deal.

(Image: GETTY)

Milan are apparently preparing in case they miss out on Costa by considering other options though.

Ibrahimovic, released by Manchester United at the end of June, is on their radar.

Milan have their eye on Pierre-Emerick Aubameyang, Nikola Kalinic and Andrea Belotti too.