The Portuguese champions need to raise funds after crashing out of the Champions League and hope to cash in with their £25million-rated star.
Central defender Luiz, 23, who also doubles up at left-back, has suffered a strained relationship with his Benfica bosses.
The star was unhappy after they rejected City's summer bid.
Now Chelsea look set to move in during January's transfer window following the long injury lay-offs to John Terry and Alex.
A Benfica insider said: "Going out of the Champions League affected our financial plans. We want to re-evaluate the situation."
You'll like it here: Silva (left) has been handed the task of twisting Luiz's arm
AC Milan have a secret weapon in their bid to sign Brazil centre half David Luiz ahead of Manchester City and Chelsea.
The Italian giants are reportedly using the Benfica defender's compatriot and close friend Thiago Silva to tempt Luiz into a move to the San Siro.
It is believed that the Portuguese champions are ready to cash in on the 23-year-old this winter after failing to progress in the Champions League.
Bids are expected to start at about £25million - an amount City were prepared to pay in the summer - but Milan hope more than money will turn the player's head.
Silva chose Italy when there was interest from Chelsea last year and the former Fluminense defender has been bending Luiz's ear on Milan's behalf, according to Italian newspaper Corriere dello Sport.
Serie A's most decorated side already have a good relationship with Benfica, especially as former Rossoneri midfielder Rui Costa is the club's sporting director.
Inter Milan president Massimo Moratti has also confirmed his admiration for Luiz, who is believed to be unhappy at the Lisbon club and refusing to discuss a contract extension.
just get mattew upson from west ham lar. he is cheap, 31 years old, just buy him as temporary measure first.
what about S'pore national team players ???
Milan could get a truckload of S'pore defenders for the same money.....................maybe even a train load........