Phil Jones is also fit again, but Sir Alex says he is more likely to be involved in Wednesday's FA Cup replay against West Ham.
Wayne Rooney could make a return against the Hammers as well having missed the last four games after picking up a knee injury.
"I'm hoping Wayne will start training today actually, in which case he won't be far away," the boss told reporters on Friday. "I don't think it's a big issue but it will help him along. The injury is quite straightforward so if he starts today we should have him available for Wednesday's game.
"Nani's back in training and will be in the squad on Sunday. Phil Jones is back, although I think Wednesday is more likely for him. Anderson has been back training for 10 days so he'll be in the squad on Sunday.
"All in all, we're in a healthy situation. How long it will last I don't know, but it's good to have them back.
"Of course, it's Liverpool, a derby game. It never changes, it's always an immensely important game and also intense and emotional," added the United manager. "Everything you can think of in a derby game will probably be there on Sunday. At least we go into the game in reasonable form."