The New Zealand international, who penned a new six-and-a-half-year deal at Upton Park last month, has not played since limping out of the 1-0 defeat to Premier League leaders Chelsea on March 4 with a hamstring injury.
However, the centre-back has returned to training and is in contention to face bottom club Leicester at the King Power Stadium.
"Following the hamstring injury he suffered against Chelsea on 4 March, Winston Reid is fit and is training hard to be ready for Saturday's Barclays Premier League fixture at Leicester City," read a statement from West Ham's head of medical and sports science Stijn Vandenbroucke on the club's official website.
Forward Enner Valencia may also travel after recovering from a toe laceration.
Elsewhere, striker Andy Carroll has taken a significant step in his rehabilitation from a medial knee ligament injury sustained against Southampton in February.
The former Liverpool man is no longer using crutches and has had his knee brace taken off, while also starting recovery work in the gym.
"I'm feeling alright. It's a lot better, getting off the crutches, out of the brace and being able to move more on the bike and do some work in the pool," he said.
"It's good to come in to work at the training ground and see the lads too. If you're working away from the club you might not see them for a while, but it's nice to come in in the mornings and have breakfast and lunch with them."
