Allardyce is desperate to bolster his attacking options after seeing West Ham struggle for goals in the absence of the injured Andy Carroll.
West Ham's co-owners David Gold and David Sullivan have promised Allardyce they will fund a deal for a new striker and the Hammers boss has confirmed they are close to landing a new addition to the squad.
Allardyce has been linked with the likes of Rickie Lambert, Obafemi Martins and Diego Forlan, but the Hammers boss refused to reveal the identity of his target.
"It is an attacking player there are no doubts about that," said Allardyce.
"We are moving on to 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 possibly can, David Sullivan is the quickest owner of a football club I have ever had. He doesn't 'ooh' 'ahh' and 'um' like most of the other owners I have been involved with."
Meanwhile, Allardyce insists he has no problem with Sullivan's comments that he regrets signing Carroll on a permanent basis in the summer with the striker yet to feature this season due to injury.
"David is the owner and he can always say what he thinks because he pays for and looks after the club," added Allardyce.
"The way he is as a person, he gets extremely anxious about the situation. The pressure comes on him as much as it does on to me and everyone else.
"Dealing with that is one thing you have to be capable of doing.
"The commitment to go forward is a big responsibility for us all because this club has to be in the Premier League when we go to the new stadium."