Belgium midfielder Fellaini was ruled out for six weeks after suffering a hamstring injury while on international duty last month.
But the the 22-year-old's recovery is ahead of schedule and Moyes believes he could even return for the Premier League game with Arsenal on Sunday week.
"The situation has improved," Moyes said in the Liverpool Echo.
"He's training well and will have an outside chance of being fit for next Sunday."
Moyes has praised Fellaini for doing everything possible to limit his time on the sidelines, saying: "The lad is probably the hardest working player when he's injured, and probably the most dedicated to getting back.
"The medical staff will say he's a pleasure to work with, he wants to put his time in and get back quickly.
"He was in Belgium doing a solid week's work and he really puts himself out."