Richard Arnold replaced Woodward as head of transfers at Old Trafford ahead of Dutch manager Ten Hag arriving from Ajax.
Former United manager Van Gaal, who worked under Woodward for two years, has made it clear he is not a fan of the 50-year-old executive.
He previously told Ten Hag to consider turning down the manager’s job because United are a ‘commercial club’ and it would be ‘better to go to a football club’.
However, Ten Hag left Ajax to take over at United last month and Van Gaal said on Tuesday: “Now there is new management. It was Woodward and now it’s Richard Arnold and that can make a difference. So we have to wait and see.
“[Ten Hag] has a lot of confidence. So who am I to say anything about it? »
Ten Hag would like to make a quick return to his former club to sign Jurrien Timber. The 20-year-old Ajax defender is part of the Dutch squad in Cardiff.
Timber is set to play Wednesday with Liverpool centre-back Virgil Van Dijk, who has been granted time off after a demanding season for club and country.
Van Gaal said Timber needs to play first-team football to make his World Cup squad later this year.
He said: “I think a player of his quality can play in the Premier League. That’s no problem. If he has to take that big step now, that’s the question.
“[If he does not play] then he is not so wise, I think. He must play. »
Van Gaal revealed in April that he was battling prostate cancer. The 70-year-old later said the “25 radiation treatments” he underwent for the condition had been successful.
“Now is not the time to talk about my illness,” Van Gaal said. “But I can assure you that I can manage because this group is a gift for me. In my career, I have never coached such a group.”
Additional reporting by PA Media.