The Italians are desperate to add a striker in the January transfer window after losing Pippo Inzaghi for the rest of the season and continuing worries about Alexandre Pato.
Milan are keen on City striker Mario Balotelli but have been told there is no chance of a deal so soon after the 20-year-old's £23million arrival at Eastlands from Inter Milan.
Roque road: Santa Cruz has found his opportunities limited at Manchester City
Sevilla striker Luis Fabiano is an option for the Serie A side, but is seen as overpriced by Sevilla at £12.5m.
Santa Cruz can leave City with boss Roberto Mancini's blessing after playing less than half an hour of Barclays Premier League football this season.
Sam Allardyce is keen to take the 29-year-old back to Blackburn and former Rovers boss Mark Hughes is keen to team up with him at Fulham, but a bid from AC Milan would be intriguing.
Loving life in Milan: Striker Robinho
Although turning down Italy's most decorated club may seem difficult, the Paraguay international would largely be providing cover for Zlatan Ibrahimovic and may be reluctant to swap one bench for another.
Lazio are also mulling over a January move after coming so close to signing Santa Cruz in the summer.
Meanwhile, Robinho appears to have no regrets about leaving City for AC Milan in the summer, after winning plaudits for a good run of form.
'I want to stay a Milan player for another 10 years,' he told La Gazzetta dello Sport.
'Serie A or Champions League? I want everything, even the Coppa Italia. This will be Milan's year,' he added.
'I like it here at Milan, this is such a great chance for me and I don't want to let it go. I love playing football in Italy because it's how I like it here.'
The Brazil international's close friend Elano, meanwhile, is leaving Galatasaray for a return to Santos in the January transfer window.
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