Despite a number of high-profile signings during the summer, Milan continue to be cut adrift from the top teams in Serie A and that has already led to Vincenzo Montella leaving San Siro.
Gennaro Gattuso is currently in charge but according to Gazzetta dello Sport, that will only remain the case until the end of the season.
The report suggests that Mancini has already been approached regarding a return to Italy, where he has spent two spells in charge of AC's rivals Inter Milan.
Mancini is currently with Russian giants Zenit St Petersburg, where he allegedly receives £130,000 per week, but Milan are hopeful that the 53-year-old could be tempted back to his homeland.
Milan currently sit in ninth place in Italy's top flight, 21 points below leaders Napoli.