Rooney has missed United's last five games after picking up a knee injury during training on Christmas, while Nani has been out since November with a hamstring problem.
But Ferguson has confirmed to MUTV that both players will feature against West Ham in the cup, and United look to set up a fourth round tie with either Fulham or Blackpool.
Fears have also been eased over injury victims from the win over Liverpool, Nemanja Vidic and Ashley Young, both of whom were replaced on Sunday.
Both players were understood to be suffering from knee injuries, and while Young will miss the next two games with the issue, Vidic picked up a concussion and is available for selection.
"Actually, Vida's knee is okay," Ferguson admitted. "It was concussion.
"He had a little bit of concussion but he's okay and fine. He trained yesterday and was good.
"There are no other serious knocks really. I think they're all pretty good. Obviously, Young has got a dull knock, a little bit of a strain on the knee, but it's nothing serious.
"I think he'll be back next week. Maybe not for Tottenham but, the week after, he should be okay."
After the pair's 2-2 draw at Upton Park, during which Robin van Persie scored a late equaliser, the replay should see former Hammer Rio Ferdinand return to the United defence against his former club.
After spending eight years at West Ham as a youth player and then as a first-team regular, Ferdinand has a special place in his heart for the club and admits the replay will be a nice occasion.
"West Ham is special for me," said the centre-back. "I look at West Ham as being a similar club to Manchester United in terms of their history and the way they keep all their people for so many years.
"Here, you see Cath on reception who has been here 30-odd years. It is similar at West Ham with Jimmy Frith and people like that. It is a club that is close to my heart because I came through the ranks there.
"I look out for their results, after Manchester United's results. I am sure it will always be that way."
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