The Lancashire club have struggled on their top-flight return and are yet to pick up a win, having scored just three goals in their seven matches thus far.
West Ham, by contrast, are benefiting from a productive transfer window and a more attacking philosophy after Allardyce's style of play was questioned by some supporters last season.
While West Ham are seventh with three wins to their name, Sean Dyche's side are second from bottom, but Allardyce - a former manager of Burnley's neighbours Blackburn Rovers and Bolton Wanderers - is not expecting an easy ride.
"The main thing for me on Saturday is to see whether the players have the mentality to remain as consistent as they have been and to see if we can get back-to-back wins for the first time this time this season," he said.
"It'll be a tough game as Burnley are a well-organised, extremely fit side who make life difficult, even though they haven't won yet.
"It'll be a big mental test and a good indicator of where we are."
Allardyce - who turns 60 on Sunday - is hopeful midfielder Mark Noble will make his return from a calf problem, while Enner Valencia should feature despite only returning from international duty on Wednesday.
However, doubts remain over the availability of Carl Jenkinson (hamstring), James Collins (groin) and Guy Demel and Ricardo Vaz Te (both thigh).
Burnley were handed a boost during the week with the news that Danny Ings and David Jones are back in contention after respective hamstring and thigh complaints.
Ings' potential comeback in particular will delight Dyche, the striker having netted 20 league goals during Burnley's promotion-winning campaign last term.
Winger Michael Kightly, who scored the first Burnley goal in the 2-2 draw at Leicester City last time out, has urged his team-mates to maintain their belief as they go in search of their maiden win in 2014-15.
"We're disappointed not to have won a game but we've got two home games after this international break and hopefully we can get a win," he told the Lancashire Telegraph.
"We just haven't had the rub of the green and we haven't got that win that we've deserved. If we can keep building and believing as a team we will get there. It's a tough division and we know that. We know it will come.
"We've got to make sure that we don't lose the belief. We haven't got a win yet, but if we keep playing like we have been then I'm sure we will."
Dyche has worries over the fitness of Michael Keane (hamstring), Dean Marney (hamstring) and Kieran Trippier (ankle), while former West Ham midfielder Matt Taylor is out after undergoing Achilles surgery.
‘Thierry Henry was my hero, but when you talk about players who have a wand of a left foot, he genuinely had that. He made my life so much easier on the right’: Ex-Arsenal star omits Gunners legend from his Perfect XI
Who is Sonia Bompastor? Everything you need to know about the Chelsea women manager
