The Chelsea midfielder could move to Upton Park yet again in the summer, on a free transfer, having been a Hammer from 2005 to 2007 before rejoining them on loan earlier this term
The Israel midfielder made only six appearances for West Ham during his second spell at the club, but with the 32-year-old's contract at Chelsea expiring at the end of the season, Allardyce revealed he is looking at potentially signing the former Hammer on a permanent deal.
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Allardyce told reporters: “There are lots of names on our list from our head of recruitment and there will be lots of people chasing those players who are not going to cost anything transfer-fee wise.
"He will be on our list probably, but we will wait and see when the time comes around.”
Benayoun originally joined the Hammers in 2005 for £2.5 million from Racing Santander, and made 63 League appearances, scoring eight goals, before signing for Liverpool in summer 2007.
He moved to his current club Chelsea - who host West Ham on Sunday - in 2010, but has found first-team opportunities limited at Stamford Bridge, and spent last season on loan at Arsenal.