The attacking duo, which has been sidelined with thigh and groin injuries respectively, is back in full training, while Marouane Fellaini has recovered from a back problem.
Netherlands international Van Persie has missed the last 11 games in all competitions because of a thigh injury but was back in training - along with Marouane Fellaini - prior to the shock Capital One Cup defeat to Sunderland.
And Rooney, who has been sidelined since New Year’s Day with a groin problem, was also back with the first team squad last week.
Moyes revealed the strike duo trained Monday along with midfielder Fellaini, who has been struggling with a back problem and also underwent surgery on his wrist.
The trio could be back in the squad when the Premier League champions face their former striker Ole Gunnar Solskjaer’s struggling Cardiff City side at Old Trafford on Tuesday.
United has endured a disappointing season so far, but Moyes now has plenty of grounds for optimism following the record signing of Juan Mata and the return of key players.
Rooney and Van Persie played an integral role as United regained the title last season, but the pair has started only 26 games between them in the top flight in the current campaign and have been sorely missed.
Mata trained with his new teammates Monday for the first time since his 37.1-million-pound move from Chelsea, but Moyes has not yet decided whether the Spain midfielder will make his debut against Cardiff.
Moyes expects Solskjaer to be given a great ovation when he returns to the club where he made his name during his playing days. The former Norway striker was a fan favorite at Old Trafford thanks to his goalscoring exploits in an illustrious 11-year career at the club, with a late winner in the 1999 Champions League final victory over Bayern Munich his finest hour.
"Ole will get a fantastic reception and deserves it. He is a legend for what he has done here," he said.