The 22-year-old Romanian international was said to be a target for Barcelona, before seeing out the summer in his homeland, but is once again the subject of more speculation, ahead of the January transfer window.
Blues boss Roberto Di Matteo is among those managers to have expressed an early interest in Chiriches, but the Champions League holders would face competition for his signature from Italy, should they attempt to lure him to Stamford Bridge.
"I can confirm that AC Milan are looking at the player," the defender's representative Viktor Becali told calciomercato.com.
"Milan's sporting director (Ariedo) Braida has seen him play several times both for the national team and for his club team.
"There is nothing concrete yet, though, and it is too early to say what will happen."
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