The 25-year-old is running down the months on his Cherries contract, which is due to expire in the summer of 2024, and Andoni Iraola's side do not possess the option to extend his stay.
Kelly has struggled to stay fit throughout the 2023-24 campaign, making seven appearances for Bournemouth in all competitions, including five starts in the Premier League.
However, the former Bristol City product wore the captain's armband in last weekend's meeting with Burnley, where the Cherries claimed their first top-flight victory of the new term in a 2-1 win.
Bournemouth's success saw Iraola's men shoot out of the relegation zone into 17th place, but they remain very much in the demotion mix and would be resigned to losing Kelly on a free transfer should they go down to the Championship.
The Englishman — who represented his nation at Under-21 level — was briefly linked with a move to Tottenham Hotspur over the summer, before the Lilywhites opted to sign Micky van de Ven instead.
Interest in Kelly's services is expected to grow should it become clear that he will not be extending his Bournemouth deal, though, and Tottenham could reignite their interest as they search for more defensive reinforcements in 2024.
However, journalist Fabrizio Romano reports that the Premier League leaders could face stiff competition from AC Milan, who have identified Kelly as an ideal acquisition for their youthful recruitment drive.
Romano states that the Rossoneri are working to bring Kelly to San Siro as early as January, which could be Bournemouth's last chance to recoup a fee for the defender before he enters pre-contract talks with foreign clubs.
Milan have
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