Neill had been seeking a new settlement, but the signs were ominous two days ago when Jackson (his agent), talking about the ongoing negotiations, said: "The longer it goes on, the more likely it's not going to happen."
Jackson also revealed that his client had rejected an initial offer because he "didn't feel it reflected his value as a player and captain".
As well as eyeing new employers, Neill is on international duty this month.
Australia have three World Cup qualifiers - away to Qatar and then at home against Bahrain and Japan - and they require just a single point to guarantee participation in South Africa next summer.
The West Ham website also revealed that Diego Tristan, Lee Bowyer, Walter Lopez, Kyel Reid, Tony Stokes and Jimmy Walker were all free to leave the club.
It added that the loans spells of Jan Lastuvka (from Shakhtar Donetsk), Radoslav Kovac (Spartak Moscow) and David Di Michele (Torino) had come to an end.
Meanwhile, it was announced on Wednesday that goalkeeper Peter Kurucz had signed a four-year deal.
The Hungary Under-21 keeper has been on loan from Budapest side Ujpest FC since February, making his debut for the reserve team against Aston Villa in March.
The 21-year-old was also named as a substitute in the senior squad for the first time at Everton last month.
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