Manager Sam Allardyce said on Tuesday that he had studied Carroll, 24, closely in training and was convinced he was almost ready to make his comeback.
"Andy's training on a day to day basis with the rehab boys and improving all the time," Allardyce told the club website ahead of Thursday's London derby at home to second-placed Arsenal.
"He's kicking, turning, twisting. He's improving all the time and I expect him back with us shortly.
"I'm not going to put days or weeks on it because I don't want to but it won't be too long," said Allardyce.
Fourth from bottom West Ham have struggled up front this season without Carroll, scoring 14 goals in 17 Premier League games.