He started just six games last term in a season blighted by injury.
Despite the departure of Kieron Trippier to Athletico Madrid this summer, Aurier is still second choice in his position.
Manager Mauricio Pochettino has opted for Kyle Walker-Peters to start the opening two Premier League games of the season at right-back.
Milan are keen on an initial loan deal for Aurier with an option to buy at the end of the season, reports Soccerlink.
The rosseneri already have Davide Calabria and Andrea Conti at right-back, but there is speculation over Conti’s future at the San Siro.
Both Parma and Werder Bremen are thought to be interested in signing the Italian international, but Sky Italia reports suggest he wants to fight for his place at Milan.
Any deal for Aurier will need to be completed by September 2 when the Serie A transfer window closes.
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