The England player has not played for the Hammers since May and suffered a fresh fitness setback this month after being struck down by a stomach infection.
Manager Sam Allardyce has revealed that Carroll is making progress in his rehabilitation, but is not expected to make a playing return before January.
Allardyce remains reluctant to rush back the 24-year-old, despite his team's lack of goals this season.
"Andy hopefully will be back with us next week to start some training," he said.
"We expected him to be back two or three games into the season, and that hasn't happened.
"We have to be tentative in our approach to it.
"When Andy's fit we've got to get him fit to stay fit.
"When he will return, I think that depends on our assessment when he does eventually come back with us.
"On a day-to-day basis he can then start to push forward.
"Having not played a game since last May, it will take some time to get him into a match-fitness situation.
"He's done an awful lot of work, but that doesn't include match fitness, so it will take a while for him to get back up to speed."
Allardyce is preparing his side for Saturday's Premier League match with Fulham, who sit next to West Ham in the table on just 10 points.
He has urged his side to take advantage of Fulham's defensive problems this season.
"My surprise is that I thought our win against Tottenham would kickus on to a good run of wins. It hasn't happened but we've got to believe we'll start putting away our chances," said Allardyce.
"We've got to start converting our opportunities.
"Against Fulham, both teams are having a struggle at the minute.
"We hope we can regain our defensive solidity and maybe exploit a defensive weakness in them, after they have leaked 12 goals in their last four games."