The Upton Park outfit have been toothless this season as they have registered just 13 goals in 16 Premier League games, coinciding with the absence of £15 million record signing Andy Carroll.
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"It is an attacking player there are no doubts about that," Allardyce told reporters.
"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."