The Nigerian striker has not played for the relegation-threatened Premier League side, since he suffered a knee ligament injury in their 2-0 loss to West Brom in January.
Moyes revealed that Anichebe is out running and says he is waiting for the medical department to give him the green light.
“We hope that Victor could be back and maybe Catts,” Moyes told SunderlandEcho.
“I think Catts could get some training in but the one we’re really looking to see if we can get back is Victor.
“There are no guarantees but I know Victor’s doing a bit more running and hopefully getting closer.
“My bigger worry is how they can get a level of match fitness to make a difference and help us in such a short time.
“I have to hope that we can get them back and give ourselves another dimension, even if it’s getting them back off the bench late on.
“I’ll probably play one [a friendly] this week because we have three games in a week coming up and we’ll need the squad of players we’ve got.”