The Senegalese forward currently plies his trade in the Bundesliga with Hannover, where he has enjoyed much success after a torrid time at Old Trafford.
Stoke have been linked with his signature over the course of the past few transfer windows, while Cardiff are also believed to be in the hunt with Ole Gunnar Solskjaer keen to add to his squad after recently taking charge of the Bluebirds.
However West Ham are ready to beat their domestic rivals with a move in the coming weeks.
The London club are currently embroiled in a relegation battle, with the lack of a top class striker for the most part of the season so far having contributed heavily to their situation.
Big money summer arrival Andy Carroll has been unable to feature due to injury, while the likes of Modibo Maiga and Carlton Cole are not seen as adequate options to fire the Irons to safety.
Diouf is thought of as a suitable focal point to Allardyce’s attack, and could be available for around £5m.
West Ham have also been linked with a loan move for Lacina Traore, who has recently joined Monaco from Anzhi Makhachkala.