Rooney has missed the last three games due to an ankle injury, but United boss Louis van Gaal confirmed on Friday the striker had been back in training for a full week.
"Three or four players are coming back," Van Gaal said.
"They have trained a full week - Rooney has, for example
It is possible he can play, but we have to wait and see."
Rooney's next appearance will be his 500th as a United player.
He has only scored once for the club since October, and Van Gaal added: "I hope when he plays he scores a goal, because it is a big day for him."
Van Gaal also revealed that defender Chris Smalling and midfielder Ander Herrera, recently sidelined by groin and hamstring problems respectively, have trained all week ahead of the Norwich match.
Meanwhile, Van Gaal has expressed his surprise at Jose Mourinho being sacked by Chelsea.
"What can I say? It was a big surprise to me, I didn't expect that," he said.
"He is a fantastic manager with a record that nobody has in this football world, but it is still possible.
"What I said in my own press conference is that the main thing is always, of course, first the results and second the chemistry between the players and the manager and staff.
"I cannot judge what was happening at Chelsea, but I was very surprised."
Van Gaal's own position is under scrutiny, with United having gone five games in all competitions without a win.
When asked if the fact Mourinho had been axed so soon after guiding Chelsea to the Premier League title showed that no manager was safe, Van Gaal said: "Yes, it is like that
But we know that in advance
Also Jose knows that
This is the world."
Source : PA
Source: PA