The 29-year-old, who made 29 league appearances for the Reds last season despite being told he was not in manager Brendan Rodgers's plans, is undergoing a medical at Upton Park, with a move set to be confirmed by Tuesday.
|7/4||West Ham are 7/4 with BetVictor to finish in the Premier League top half
"It hasn't quite worked for him at Liverpool and he has lost his way a bit but I think what Sam will do, and is good at, is put an arm around him, tell him how great he is and put him in the first team, and I think potentially he could be a really good buy for the club.
"The club have stated their intentions by signing Andy Carroll and looking to sign the likes of Stewart Downing, because it is a lot of money to spend. They are looking to push on.
"I don't expect them to qualify for Europe but they finished 10th last year - why can't they finish ninth this year and push the club forward?"
Allardyce's side begin the new season on Saturday against newly promoted Cardiff City.