Moyes had promised to deal with the Englishman after he headed down the tunnel early during West Ham’s defeat at the hands of Manchester City last Sunday, having been left an unused substitute.
Carroll reportedly had refused to apologise for his actions after the squad were given Tuesday off, but the Evening Standard believe he returned on Wednesday and apologised to Moyes and his fellow teammates.
After their loss to Premier League champions Manchester City, the Hammers sit in 15th place, just three points clear of the drop zone, with home games against Manchester United and Everton still to play.
Andy Carroll has only started seven Premier League matches this season, making another seven appearances off the bench. His goal tally currently sits at three, making him the sixth top goalscorer at the club this season.
Carroll’s season has been stung with multiple injury woes, after sustaining a serious ankle problem earlier in the season.
The dominant forward signed for the Hammers on a permanent basis back in 2013 for a then club record transfer fee, thought to be in the region of £15m, and has since mad 88 appearances for this club.