England manager Roy Hodgson says he had concerns about Luke Shaw's fitness before Manchester United boss Louis van Gaal publicly criticised the left-back.
Van Gaal said Shaw, 19, was "not very fit" during United's pre-season tour.
"[Shaw] might have had it mentioned to him a couple of times during the World Cup by people like myself and [physio] Gary Lewin," said Hodgson.
"If Louis thinks that he can get him fitter then I'm sure he will certainly have our approval."
United bought Shaw for £27m from Southampton this summer but Van Gaal made the player train on his own on their tour of the United States.
Shaw is currently out of action with a hamstring injury and is not part of the England squad for the forthcoming internationals against Norway and Switzerland.
Hodgson added: "I must say watching him play in the matches for Southampton, he didn't seem to have too many problems coping with the physical side of the game."
Meanwhile, Van Gaal has hinted changes may be imminent at Old Trafford.
United have picked up just one point from two Premier League matches under their new manager and were knocked out of the Capital One Cup on Tuesday by League One MK Dons, who pulled off a shock 4-0 victory.
And with the transfer window closing on Monday, Van Gaal suggested there might be arrivals and departures.
"I had a conversation with the players and I said maybe after this weekend we shall have another group, because players shall go away and others shall come in," he said.