Van Gaal led United from 2014 to 2016, winning the 2016 FA Cup before being sacked two days later with Woodward in charge as the club’s vice-chairman at the time.
The 70 year-old Dutchman has been critical of United in the past for being too commercially focused, rather than being a football club.
Woodward had been at the helm at Old Trafford from 2012 until February this year, with Richard Arnold replacing him in the lead-up to Ten Hag’s appointment as the club’s new manager in April.
Ten Hag, who joined United from Dutch champion Ajax, faces a stern challenge reviving the club which has not won silverware since 2017, but Van Gaal believes change at the top may help his cause.
"There is now a new leadership," Van Gaal told reporters ahead of the Netherlands’ Nations League game with Wales in Cardiff. "It was Woodward, now it's Richard Arnold, and that can make the difference so we have to wait and see.
"[Ten Hag] has a lot of confidence, so who am I to say something about that?"
Upon his appointment as United boss, Ten Hag had rebuffed Van Gaal’s claims about the club being too interested in commercial affairs.
"I draw my own line and I’m convinced that is not the case," Ten Hag said. "I spoke to the directors about it and football is one, two, three these days."