Higginbotham, 34, who has made 12 appearances for the Championship club, now looks set for a move elsewhere after rival clubs showed interest in his services.
Manager Mick McCarthy told Ipswich's official website: "We had agreed a deal with Danny to stay but there has been interest in him from other clubs.
"That comes as no surprise as he's a terrific professional and that's why we wanted to keep him here.
"He wants the chance to earn a permanent move and preferably something which is closer to his home.
"I can understand that and if it works out for him then I wish him all the best of luck."
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