De Jong comes off contract at the end of the month.
DHA says the Istanbul club are desperate to sign the 30-year-old midfielder ahead of their Champions League entry next term.
Manchester United are hotly tipped to bring De Jong to Old Trafford, providing he accepts a bit-part role.
Boss Louis van Gaal is clearly a fan of the midfield enforcer having selected him for his the Netherlands' 2014 World Cup squad.
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