Cole was released at the end of last season after failing to agree a new deal at Upton Park but the striker that splits opinion among Eastenders is set to get another chance.
West Ham failed to make the required signings in the summer and with Andy Carroll out until the new year, Cole will join Modibo Maiga and Mladen Petric as the first team strikers.
Cole is set to play in a couple of training games to get his match fitness up before signing a deal until Christmas after no other club came in for him.
‘In terms of a contract as soon as he’s fit there will be the offer of short-term contract – that’s why he’s here and trying to improve fitness,’ Allardyce said.
‘As soon as he’s OK – as long as the terms and conditions are right – he’ll be with us until however long that contact is.
‘He’s been here on a day-to-day basis. Beauty of this football club it kept him fit for a long time.
‘He’s got certain training programmes to suit him to make him available for a Saturday afternoon. It will be a matter of days. Couple behind closed doors games and take it from there.’
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