Maja, who is the Black Cats' top scorer with 15 goals in all competitions, is yet to sign a new deal at the Stadium of Light.
His current contract is set to expire in the summer and, despite the club offering him much-improved terms, he is yet to commit his future to Sunderland.
A deadline was set for Maja to reveal his intentions and, after initially indicating he was prepared to sign, his agent advised him not to sign the offer on the table.
Sunderland owner Stewart Donald revealed the news on Twitter, saying: "Yesterday Josh asked to see Jack to say he will sign.
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"Today I got a call from Sky TV saying he won't sign.
"Josh advised his agent has said don't sign but no courtesy to tell the club - Also we offered what the agent indicated!!! Busy January ahead."
He went on to add: "Stay behind him and don't get up his back - we will try & change his mind."
That news has prompted a frenzy of reports of fresh interest in the striker, with Crystal Palace and Huddersfield Town two of the latest top flight clubs thought to be eyeing the striker.
But perhaps the most interesting link is that to Newcastle United, with the Daily Mail claiming that the Magpies are ready to line-up a surprising £5million bid for the striker.
Rafa Benitez is keen to add attacking reinforcements to his squad but is expected to be forced to work on a limited budget during this winter window.
Manchester City, Tottenham, Everton, Southampton and Middlesbrough have all been linked a move for Maja in recent months.