The towering centre-back, who has made more than 100 league appearances for the club since arriving from Bayer Leverkusen in 2004, is believed to be unsettled by the fact that he will not be assured of a first-team place next season.
And the news is thought to have alerted the cash-rich Blues, who are expected to fail in their attempt to lure Chelsea and England captain John Terry to Eastlands this summer.
Lucio - who has won 84 caps for his country - is not the first Brazilian Bayern Munich player to be linked with Mark Hughes' side during the close-season, with midfielder Ze Roberto eventually opting to choose Hamburg over City.
And Bayern boss Van Gaal has insisted that the Blues would also be wasting their time trying to sign Lucio.
"Lucio is under contract just like Martin Demichelis, Daniel van Buyten and Breno," he told Suddeutsche Zeitung.
"These four defenders all have a strong right foot and are competing with each other for one first-team spot.
"I am, however, just imagining that there will be one starting berth available to these four players."
NEWS: Hamburg seal Ze Roberto signing
NEWS: Ze Roberto tipped for City switch
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