Carroll has not represented the Hammers since suffering a knee injury in August, and last month Bilic admitted that the Englishman's recovery had been "longer and slower than expected".
The 27-year-old has since returned to first-team training, however, and Bilic is hopeful that the powerful forward will be fit to face Man United ahead of this weekend's Premier League clash with Arsenal.
"We're going to see today whether Andy Carroll is ready, we will make a decision after training. Maybe tomorrow, definitely Saturday," Bilic told reporters.
Man United and West Ham played out a 1-1 draw in the Premier League at Old Trafford on Sunday afternoon.