Jlloyd Samuel impressed in West Ham's friendly win over Real Zaragoza and is set to hold talks with boss Sam Allardyce over a possible deal.
The full-back is available on a free transfer after leaving Allardyce's former club Bolton and featured in Saturday's 2-0 success against Zaragoza.
"First impressions were really good," assistant manager Neil McDonald told the club's official website.
"Jlloyd has got a good pedigree and a good CV, so we've got him in, trained him for a couple of days and got a good look at him on Saturday.
"He's enjoyed what he's done and we've enjoyed having him, so I'm sure the manager will sit down with him and see what the situation is later on at the start of next week."
McDonald added: "I think Joey is a decent defender and very good on the ball as well.
"He's big and strong, so he's a great addition and gives us some fantastic competition for places, which is great."