The England striker has not featured for the London club since completing a big-money permanent move from Liverpool.
Carroll made a big impact during a loan spell at Upton Park last season, but suffered a double fracture of his right foot while he was closing in on a return from a heel problem and has therefore played no part this term.
The former Newcastle United man has been sorely missed by Allardyce, with West Ham struggling for goals and hovering perilously above the Premier League relegation zone.
Stewart Downing (Achilles), Winston Reid (ankle), Ricardo Vaz Te (shoulder) and Mladen Petric (calf) are also sidelined, but Allardyce can see light at the end of the tunnel ahead of the Boxing Day visit of Arsenal.
He said: "All the injuries are progressing very well. Andy is improving all the time and we expect him to be back among the lads very shortly.
"Vaz Te will be training shortly, Winston Reid is another few weeks away, but Kevin Nolan is back from his suspension."
West Ham have lost their last six games against Arsenal, but Allardyce is plotting to take a leaf out of Chelsea's book and not let Arsene Wenger's title hopefuls settle into their passing game.
Chelsea held Arsenal to a goalless draw at the Emirates Stadium on Monday night and Allardyce is determined to thwart West Ham's London rivals in a similar manner.
He said on Tuesday: "Arsenal had a very tactical game last night. The lack of excitement in both boxes was probably down to the conditions.
"We got tumbled over twice by them last year, particularly at the Emirates, so we'll protect ourselves on Arsenal's abilities and then try to exploit their weaknesses."
