Shaw has endured a difficult start to life at Old Trafford since his move from Southampton in the close-season.
Van Gaal made the 19-year-old train on his own during the tour of the United States because he felt the defender had turned up to pre-season out of shape after playing for England at the World Cup.
However, the Dutchman was happy with the way Shaw battled his way back to full fitness, and had it not been for a hamstring injury he picked up just before the start of the season, the England left-back would have played in the club’s opening two Premier League games.
Given that Shaw has been out for a fortnight, it was a surprise to Van Gaal when Hodgson spoke about the defender’s fitness during a press conference on Thursday.
“If Louis thinks that he can get him fitter then I’m sure he will certainly have our approval,” said Hodgson, who also claimed he told the player his fitness was not up to scratch at the World Cup.
The comments irked Van Gaal, who told the England boss not to get involved in United’s business.
“He is not fit now because he is injured,” Van Gaal said.
“Roy Hodgson cannot judge at this moment. He cannot judge him because I have never seen him here at a (United) training session.
“I think he is referring to the World Cup. It is possible, I don’t know. That is what I want to ask. But now Shaw is doing a great job.
“I have read nasty articles about Shaw.
“In the United States I said to him ‘you came and you were not fit’.
“I changed his programme and he did everything that he has to do to be fit.
“Now he is an example in the dressing room. He is training fantastically.”