Anichebe was ruled out for 10 weeks after sustaining a medial ligament injury in January.
Despite being ruled out for 10 weeks, there have been fears that the striker could miss the rest of the season.
Moyes has however revealed that the 28-year-old is expected to return to action in early April.
"I’m hoping that getting Victor back at the beginning of April, we’re looking sort of another three weeks," Moyes told The Chronicle.
"Could he be back [for Watford]? I hope so but I’m not quite convinced."
Anichebe who has scored three goals in 11 appearances for Sunderland this season has struggled with injuries for most of his professional career.
The latest which he suffered in Sunderland’s 2-0 Premier League loss at West Brom on Saturday, January 21, was tough for him to take.
The Nigeria international revealed that was reduced to tears after a scam confirmed his injury.
“I don't usually cry like that but this has been a really hard one to take as I feel so settled here and know I'm important to the team,” he wrote in an Instagram post in January.
Anichebe joined Sunderland on a free transfer deal after he was released by West Brom.