The 31-year-old is out of favour at the Nerazzurri, and as a result has been the subject of much speculation over the past few weeks, with the likes of PSG, Chelsea and Madrid rumoured to be interested in acquiring his services.
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The Brazilian's agent confirmed that his client feels "It is time to move on", and the player has not been included in the San Siro club's Europa League squad for their qualifying tie with Hajduk Split.
Reports suggest Carlo Ancelotti's PSG put in a bid of around €8-10 million (£6.3-8m) for the Brazil international, an offer that would have been readily accepted by Massimo Moratti as he looks to fund an offer for Sao Paulo youngster Lucas Moura.
But Maicon is not keen on a move to the Ligue 1 side, and instead would prefer a switch to La Liga champions Madrid, or Champions League winners Chelsea.
His contract expires at the end of next season and there has been little movement from the San Siro side in offering the player an extension.
Maicon, who represented Monaco for two seasons before moving to the Italian giants in 2006, may even extend his contract in Lombardy, but that option, according to the reports, remains very much unlikely.