The attacker, who plays on the left-hand side, was eager on a return to the Premier League.
Transfer expert Fabrizio Romano reports that the Hammers are in advanced talks with Villarreal for a transfer.
However, they have failed to agree personal terms with Danjuma.
At present, the transfer is off, but that may change if Danjuma lowers his wage demands.
West Ham may move on to other targets if a deal cannot be struck in the coming days.