Milan are not the only club interested in Aurier – his former team and French champions Paris Saint-Germain are also reported to have enquired.
The Ivorian is believed to have asked Spurs to sell him, after appearing just 41 times in the two years since his £25 million arrival.
The competition for the right-back spot at Spurs is unforgiving, and is what pushed Kieran Trippier to join Atletico Madrid this summer.
Kyle Walker-Peters is now the preferred option for Mauricio Pochettino, and Aurier looks set to be condemned to the substitutes' bench once again.
Milan are thought to be more of an attractive proposition than PSG for Aurier, who wants as much playing time as possible.
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FourFourTwo Podcast, Episode #11: Chernobyl – the lost football club
Pep Guardiola issues a very blunt answer when quizzed by reporters on latest accusation levelled against Manchester City
'I think my opinion is more important than Roy Keane's. I know as a captain he does things sometimes with his arms, criticising his team-mates, but most of all it's a bit of frustration.' - Ruben Amorim hits back in Bruno Fernandes row
