The 32 year-old is available from Newcastle this month and is wanted by the Hammers.
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The Daily Mail says Newcastle will do business with the Hammers, but want to find a replacement for Lascelles first.
Before their FA Cup win against Bournemouth last week, Toon manager Eddie Howe confirmed: "He is not training with us currently.
"He hasn't felt well enough physically to train. I don't think he is injured particularly but his body isn't ready.
"There is a possibilty he could leave but Jamaal has been an excellent leader for us over the years behind the scenes."