Carroll, 28, missed the Hammers' last game, a 2-2 draw with West Brom, due to a groin injury. Speaking at a press conference on Thursday ahead of the trip to Vicarage Road, manager Slaven Bilic has not ruled out his striker returning in time for that match, but is wary of rushing him back too soon.
"Regarding the game against Watford, he'll try to run today (Thursday) and if he's good then maybe he has a chance to be in the squad for Saturday. To be fair I don't think about Chelsea now," Bilic said.
"I don't want to rule him out for Watford. With Andy you never know, if he can run today and train tomorrow then maybe he will be in the squad for Saturday.
"This is not a big injury but he needs to play, he needs to be available and hopefully he will train tomorrow, whether he will be available for Saturday, that would be great but if not definitely Chelsea.
"He didn't train yesterday but he was in the gym for an hour and a half. He's a big lad, he gives everything and he is looking after himself."
Aaron Cresswell meanwhile has returned to training having recovered from a knock suffered in that 2-2 draw with West Brom. Andre Ayew is also pushing for a return to the starting XI. The club's record signing has endured an injury-hit first season, having also left to represent Ghana at the Africa Cup of Nations, but has been training with the first-team for the last two weeks.
Angelo Ogbonna and Diafra Sakho remain sidelined with respective knee and back injuries.