The Dutch striker is poised to return from his extended World Cup break, but Marouane Fellaini and Jesse Lingard are also sidelined for Louis van Gaal's side.
The striker missed United's 2-1 defeat to Swansea City on Saturday as he was short of match fitness having been granted an extended break following the World Cup.
Herrera, who made his United debut at Old Trafford last weekend, has been ruled out by Van Gaal, while Rojo, who joined the club from Sporting in a 20 million euro deal on Wednesday, has not yet been granted a work permit and will miss the trip to the Stadium of Light.
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Jesse Lingard was handed a start by Van Gaal on the right flank against Swansea but was forced off after 23 minutes with a knee injury. Marouane Fellaini suffered an ankle injury during training earlier this week and joins Michael Carrick on the sidelines.
"Robin is ready to play, so that's a big benefit to the team. I'm very pleased that he is able to play," Van Gaal told MUTV. "In theory [Rooney and Van Persie] could be a very good couple, they can score a lot of goals and I hope they can show that."
"Carrick from the beginning, but now also Herrera and Fellaini and Lingard — these four midfielders are injured, so we are thin in midfield now. Last week we have nine injuries, now we have seven. It is much too much. I think I never have had this as a manager, it's the first time but we have to live with this."