The 26-year-old Durham-born attacker has enjoyed six good seasons at the London Road Stadium since arriving from Gateshead back in 2004.
Since then, the ex-Newcastle United and Blyth Spartans man has made 240 appearances for Peterborough in all competitions, netting 62 times.
Maddison had previously been linked with a move to the Stadium of Light in the summer but has attracted the interest of Championship clubs Middlesbrough and West Brom during this window.
Black Cats supporters had hoped their club would make a move to sign the tricky attacker – a Sunderland fan growing up – after it was revealed his contract will expire this summer.
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However, that move now looks unlikely. Peterborough United’s chairman took to Twitter to confirm Posh have accepted a bid from Charlton.
He said: “As of this morning @theposhofficial [Peterborough United] has accepted a bid from @CAFCofficial [Charlton] who have permission to talk terms with the player.
“Two other Championship clubs have bid for the player multiple times and do not currently have permission to speak to the player.”
He continued: “Multiple news outlets have contacted me yesterday and today re knowing the details hence with all the speculation over the weekend I felt it right our fans know Current situation. There will be no more comments from me/club after today re this. Thanks.”