The centre-back has entered the final 12 months of his contract with the Cherries.
Kelly, 25, was a deadline day target of Tottenham earlier this year.
Spurs saw a £20million bid turned down by Bournemouth.
Ange Postecoglou‘s side reportedly intend to come back in for Kelly in January.
But they are set to face fierce competition.
According to Italian outlet Tuttosport, AC Milan are keen on signing Kelly.
Clubs overseas can begin negotiating with the former Bristol City ace in January, and could even seal a pre-contract deal.
Juventus are also claimed by 90min to be monitoring Kelly, as well as Borussia Dortmund.
While Liverpool, Newcastle, Fulham and West Ham are also “keeping tabs”.
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Kelly has made six Premier League appearances so far this term.
He skippered the Cherries to their first win of the season against Burnley last time out.
The former England youth international joined Bournemouth from Bristol City in a £13million switch in 2019.
Kelly has subsequently played 123 times for the Cherries, helping them to promotion from the Championship in 2022.