The midfielder suffered a hamstring problem during last weekend's 2-1 defeat against Liverpool at Upton Park.
Nolan will undergo a late fitness test tomorrow night before the game at the Emirates Stadium.
"Kevin Nolan is our problem at the moment," Allardyce told the club's official website. "He came off with a hamstring against Liverpool. Obviously that's one that we have to be very careful about.
"It's unusual for Kevin to sustain a muscle injury, I think it's the first of his career, but we'll be very careful about how we handle him. Kevin is going to desperately want to play, so we'll probably wait until tomorrow to see how he is."
West Ham are currently in 11th place in the Premier League table.