Manager Sam Allardyce said the Premier League strugglers would be much closer to safety if they had someone they could rely on to bang in the goals.
Saturday's home draw moved West Ham on to 14 points from 16 games this season, just above the drop zone in 17th place and a point ahead of London rivals Fulham and Crystal Palace, who have replaced their managers in recent weeks.
England international Andy Carroll is yet to have a kick this season because of a foot injury, while Modiba Maiga has not scored in 11 appearances and Carlton Cole only once in six.
"We all know that the goal factor is the problem for us and we would be higher up the league if we could score more," Allardyce was quoted as saying by British media on Monday.
"Creative players were on the field against Sunderland but they didn't play at their creative best."
The under pressure former Bolton Wanderers and Newcastle United manager, whose side have won once in nine league matches, knows reinforcements are needed as soon as the transfer window opens on Jan. 1.
"We are talking with a club and a player's agent to see whether they are going to join us or not," Allardyce said.
"It's an attacking player. We're trying to do the deals as quick as we possibly can.
"David Sullivan is the quickest owner of a football club that I've ever had. He doesn't 'ooh, ahh and um', like most of the other owners I've been involved with."
Being quick does not mean being right, though.
Sullivan told the BBC prior to Saturday's game that he had regretted signing the injury-prone Carroll, who has struggled for goals following a 35 million pounds ($56.97 million) move from Newcastle United to Liverpool in January 2011.
He managed just seven for the Hammers last year on a season long loan from Liverpool before he became the Londoners' 15 million pounds record signing in June.
"When we signed him we were assured by the medical staff that the very, very latest he would be back was Sept. 1. That would have meant he would only miss two league games," Sullivan said.
The owner's mood would not have been helped by Saturday's display where Sunderland, who have amassed just nine points, came close to victory after dominating possession and keeping West Ham keeper Jussi Jaaskelainen busy.
Allardyce acknowledged Sullivan's relegation fears, with the Guardian newspaper saying the club needed to clear debts of 70 million pounds before moving to their new home at the Olympic Stadium.
"He's in a position where he gets extremely anxious about the situation," Allardyce said of Sullivan.
"That's the way he is as a person. The pressure comes on him as much as it comes on me and everybody else and dealing with the pressure is something that we've all got to be capable of.
"The commitment going forward is a big responsibility for us all, especially them (Sullivan and David Gold) as the owners, because going into the new stadium this club has to be in the Premier League.
"So we have to make sure we have a team that is capable of staying there. At the moment we're not quite there but I think that's down to the injured players. We have to get them fit and do what we can until then or until we get new ones in."
($1 = 0.6143 British pounds)