Reid is suspended for Saturday's match against Stoke, having picked up his fifth booking of the season at Goodison Park.
The international break means the Hammers will not play again until the derby against Tottenham on November 19, and the Hammers believe Reid could be fit to play at White Hart Lane.
News of Reid's lay-off was revealed today by New Zealand head coach Anthony Hudson as he explained why he had not called up the defender for the home and away World Cup qualifiers against New Caledonia.
"We've been monitoring him since the weekend ... he is going to be out for the next few weeks," said Hudson. "The worst thing you can do with hamstring injury is jump on a plane.
"I understand it's important for Winston to be here but from a footballing point of view he is injured and we have squad capable of winning the games, that is the most important thing."