The Hammers are weighing up another bid for Reading striker Shane Long after their initial offer was turned down last week, and are also understood to have registered an interest in Everton's Jermaine Beckford.
However, a more likely option has emerged as former Chelsea forward Mikael Forssell is on trial with the club and could get a run-out against Sutton United on Tuesday.
Allardyce has already brought in Kevin Nolan, Matt Taylor, Abdoulaye Faye and Joey O'Brien and is considering handing a fifth former Bolton player, full-back Jlloyd Samuel, a contract after his recent trial.
But he is desperate to add to his forward line, especially with Carlton Cole's future still uncertain.
"I can say for certain we will at least bring in another striker," Gold told the club's official website. "We will leave not leave a stone unturned to get the players Sam wants, as was the case with those we have already brought in."