The midfielder has been a revelation this season under coach Max Allegri.
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The Belgium midfielder has been a key influence on Milan's revival, with the Rossonero sitting second a point behind Serie A leaders Inter Milan.
Saelemaekers' current deal runs to 2027 and MilanNews.it says the new contract will include an extension and pay-hike.
Currently on €1m-a-year, the midfielder has accepted Milan's offer of €4m-a-year to re-sign with an announcement due.
