The Upton Park outfit have been toothless this season as they have registered just 13 goals in 16 Premier League games, with only Sunderland, Crystal Palace and Cardiff City scoring fewer.
Part of West Ham's troubles can be attributed to the absence of close-season signing Andy Carroll, who has yet to make an appearance this season due a heel injury.
The striker scored seven goals in 26 Premier League appearances during a loan spell at the club last season, and his all-round displays prompted West Ham to shell out a reported £15 million for his services.
Co-owner David Sullivan has since said the club has "regrets" over the deal due to Carroll's injury woes, but he still appears to be backing Allardyce in the transfer market with the former Blackburn Rovers boss set to bolster his attacking ranks in the January transfer window.
"It is an attacking player there are no doubts about that," Allardyce said.
"We are moving onto the next phase and we are talking to the club and the player's agent to see if he is going to join us or not.
"We will try and do the deal as quickly as we can, David Sullivan is the quickest owner of a football club I have ever had.
"He doesn't 'ooh', 'aah' and 'um' like most of the other owners I have been involved with."
