Striker Carroll has scored four goals in his last four matches to prompt talk of a Three Lions call-up for next month's games against Germany and Lithuania.
England boss Gareth Southgate went to the London Stadium to run the rule over Carroll against West Brom a fortnight ago, only to find he was missing due to a groin problem.
And the 28-year-old, whose last cap came in October 2012 due to a succession of injuries, has not trained since and remains a doubt for Saturday's trip to Watford.
Hammers manager Bilic said: "When he's fit and playing Andy is a top striker.
"This is not a big injury but he needs to play, he needs to be available.
"I told him that the small things that are ruining, or affecting, his return, are no good for him, for us, or for a call-up.
"A similar thing happened last year, he was great at the beginning of the year, against Southampton and Liverpool he slaughtered them, but then he got injured and was out for a few weeks.
"Unfortunately this is a little bit slower than we expected and hoped for. Regarding the game against Watford, he'll try to train and if he's good then maybe he has a chance to be in the squad for Saturday.
"With Andy you never know, if he can train tomorrow then maybe, maybe, he will be in the squad for Saturday."
Carroll travelled with the rest of the Hammers squad to Dubai last week for some warm-weather training.
And Bilic also hopes some of the quieter members will reap the benefits of a spot of team bonding.
"It was a very good trip, we trained very hard, more than if we had stayed here," he added.
"We were all together and we all trained once a day. We used it to do a bit of fitness, intensive small games, some work on defence, it was all good.
"The team bonding is good for the players who didn't open themselves totally, who come to training and just talk to your best friend and then go home.
"This was a bit different, you are together 24/7 and you open yourself to the whole team. That was really good."
