Le 10 Sport suggests Atletico Madrid midfielder Koke and Cruzeiro's Everton Ribeiro are Moyes' two top January transfer targets - and he wants them both.
Both central midfielders, the report claims Moyes has identified the position as the chief area in urgent need of improvement.
United made just one significant summer signing, the acquisition of Marouane Fellaini from Everton, but the Belgian international will need time to adapt to the style of play.
And the likes of Anderson and Tom Cleverley have exposed a worrying lack of depth for United in central midfield.
Moyes was in attendance at the Vicente Calderon earlier this week, with Spanish newspaper Marca reporting the United boss was scouting Koke.
As for Ribeiro, the 24-year-old midfielder recently admitted it would be a dream to play for the defending Premier League champions.
The Daily Express reported yesterday that Moyes would only choose one of Koke or Ribeiro, with concerns their styles of play are too similar.
But the French report claims the United boss could look to shake things up in January and bring both midfield reinforcements in.