The winger was instrumental as Milan won their first Serie A title in 11 years last season, scoring 11 goals and providing eight assists.
And according to Italian newspaper Corriere della Sera (via the Daily Star), the Blues are at the front of the queue for the Portuguese's services.
Leao joined Milan from Lille in the summer of 2019 and has gone on to make over 100 appearances for the club. Transfermarkt currently value him at £63m – but the Rossoneri are said to want more than €100m (£87m) for one of their star men.
The 23-year-old has notched four goals so far this term, including a brace as Milan came from behind to beat arch-rivals Inter 3-2 last month.
Versatile enough to also operate as a centre-forward, Leao made his senior debut for Portugal last year and has earned 11 caps to date.
He played in both of his country's Nations League games during the recent international break and will hope to be on the plane to this winter's World Cup, which would be his first major tournament.
Leao looks set to feature against Chelsea on Wednesday night: Milan travel to Stamford Bridge on Matchday 3 of the Champions League.
Stefano Pioli's side have won one and drawn one of their two group matches so far, while the Blues are still chasing their first victory after losing to Dinamo Zagreb – a result which cost Thomas Tuchel his job – then drawing with Red Bull Salzburg in Graham Potter's first game in charge.
More Chelsea stories
Elsewhere on the transfer front, Chelsea could reportedly battle it out with Liverpool for Borussia Dortmund and England star Jude Bellingham and MLS wonderkid Jhon Duran.
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Tom Hancock started freelancing for FourFourTwo in April 2019 and has also written for The Analyst and When Saturday Comes, among others. He supports Wycombe Wanderers and has a soft spot for Wealdstone. A self-confessed statto, he has been known to watch football with a spreadsheet (or several) open...