The West Ham boss can call on striker Andy Carroll, as the England international has served his three-match ban after controversially receiving a straight red card against Swansea City on February 1.
Carroll was dismissed by referee Howard Webb when he appeared to catch Chico Flores in the face with his arm, and an FA tribunal upheld the ban after West Ham's initial appeal had failed.
Speaking ahead of Saturday's trip to Merseyside, Allardyce put forward Carroll's case for inclusion in England's FIFA World Cup squad later this year, even though the 59-year-old was unable to guarantee him a place in his own starting XI.
Allardyce's dilemma centres on whether to recall Carroll or to retain faith in Carlton Cole, who has led the line admirably in the ex-Liverpool man's absence and scored in last weekend's 3-1 victory over Southampton.
Whoever gets the nod will play in a team brimming with confidence following a superb upturn in form, with West Ham having won four straight Premier League games to take them up to 10th in the table and alleviate fears of relegation.
The Londoners have scored nine times in that run while conceding just once, and have kept the most clean sheets in the division this season with 13 shut-outs in 27 outings.
By contrast, Everton have lost three of their last four Premier League matches, albeit with those defeats all coming away and against teams in the top five in the form of Liverpool, Tottenham and Chelsea.
If recent history is anything to go by, however, then the seventh-placed Merseysiders can head into this fixture full of optimism.
Everton have gone 11 top-flight games without defeat against West Ham, and won the reverse fixture 3-2 back in September.
Nevertheless, manager Roberto Martinez says his side have to perform to their maximum capacity in order to defeat a much-improved West Ham side this time around.
"We know we will have to be at our best. They have shown that continuity at the club has paid off incredible dividends. This is a very good moment of form for West Ham," the Spaniard said.
Everton will be without captain Phil Jagielka (hamstring), while striker Lacina Traore is also absent with a similar issue.
However, Martinez can include striker Romelu Lukaku, who returns from a three-match lay-off with an ankle injury, while Antolin Alcaraz is also back in contention following a muscle problem.
Allardyce, meanwhile, is without on-loan Roma striker Marco Borriello (calf).
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