Shaw suffered a double leg break against PSV Eindhoven earlier this term, while Valencia and Rojo recently underwent surgeries for foot and shoulder injuries, respectively.
The trio are expected to be out of action for a number of months yet but van Gaal believes they are doing well.
When asked if the players were making good progress, the Dutchman said: ”I think so.
”They are, all three, going very well. Shaw and Valencia also had a holiday break and they have come back very brightly and they have the spirit to continue so that’s also very good. Rojo was here and shall also have a break at the end of January when it is possible for him. But it is going very well.”
The absence of Shaw, Rojo and Valencia has forced van Gaal to shuffle things around at the back and United’s defensive record has suffered as a result.
Ashley Young has been playing at right-back in recent weeks while Matteo Darmian has been played on both flanks over the course of the campaign. Youngster Cameron Borthwick-Jackson, too, has been thrown in at the deep end. Unfortunately, van Gaal will have to continue with a makeshift back four against Sheffield United as Phil Jones has now picked up an injury.