Premier League: Manchester United's Louis van gall unhappy at Roy Hodgson
The United left-back is currently out with a hamstring problem but his club manager says that has nothing to do with his general fitness.
Hodgson recently voiced concerns over Shaw's fitness which followed Van Gaal's decision to make the 19-year-old train on his own in pre-season.
"Roy Hodgson cannot judge at this moment," said Van Gaal.
"I have never seen him here at a United training session."
Shaw will not be part of the England squad for the forthcoming internationals against Norway and Switzerland.
"If Louis thinks that he can get him fitter then I'm sure he will certainly have our approval," Hodgson said.
Van Gaal believes the comments were inappropriate after Shaw worked hard to put his early-season fitness concerns behind him.
He added: "I think Roy 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."
Meanwhile, United's bad start to the season continued with a 0-0 draw at Turf Moor against newly promoted Burnley.