Reid was due to fly out at the start of the week and join up with the New Zealand squad who were preparing for their game against Tahiti in Papeete on Saturday.
But the 24-year-old is hoping to get the all-clear to travel out on Tuesday and wants to play some part in the double header against Tahiti - with the return game in Christchurch just three days later.
West Ham will be reluctant to send Reid to the other side of the world if there is an injury concern, but under FIFA regulations, they might not have any choice.
New Zealand Football chief executive Grant McKavanagh said: ''We're very hopeful of getting him down, if not directly to Tahiti to play then down for the Christchurch game.
''Winston wants to be here, he's just got to get through the scan and make sure there's nothing untoward in it. It's pretty positive.
''From Rick's (coach Ricki Herbert) point of view, one of the things we're looking at is continuity with this team, between now and next November. It's pretty important to get the unit together playing as regularly as possible.''