The striker only resumed training this week following his latest injury lay-off, a three-month absence with a knee problem.
But manager Slaven Bilic is considering including the 27-year-old in his squad at Old Trafford as he bids to turn around their stuttering season.
"He's been training with us for three days," said Bilic. "He came back after a long injury and he's very close.
"He could be in the squad. We're going to see, because we are not talking about two weeks of training so we can say definitely. It has been this week, so we'll see."
Carroll's West Ham career has been one constant injury battle after another, and he has missed 83 games since he joined permanently for £15million from Liverpool in 2013.
But when fit Bilic knows he has a potent attacking weapon and one who could help haul the Hammers up the table following their poor start to the campaign.
"Last year, before he got injured, when he was fit he makes an impact on a game, no matter who you play against," added Bilic.
"It's very hard to play against him. The things he is giving us are great. But we've been talking about this since I came to West Ham.
"It's a shame because you don't see it coming, only when you look at his record on paper. You don't see in training and in games that he has got problems.
"But unfortunately it has happened a few times."