United, beset by injuries since the start of the season, have won just four of their first 11 Premier League games under the Dutchman, while the summer departures of Nemanja Vidic, Rio Ferdinand and Patrice Evra have also left the squad short of experience and quality in defence.
But earlier this week Woodward told investors during a conference call to discuss United's latest financial results that the club will not go looking for "short-term fixes" in January, and Van Gaal agrees with his executive vice chairman.
“I don’t think that he has said he should not buy. I think he has said that in January it’s very difficult to buy players who are good enough for the quality of Manchester United and because of that we are not buying and I agree with that,” the Dutchman told reporters.
“When you buy it has to be a player better than you have in your squad and it shall be very difficult to find such a player in January. So that is what he wanted to say I believe and believe we are speaking the same language.”
One man repeatedly linked with a move to Old Trafford in the New Year is Roma midfielder Kevin Strootman, and earlier this month Goal revealed that the 24-year-old has told the Giallorossi he wants to make the move.
But Van Gaal refused to be drawn on whether United will try to tempt the Serie A title contenders into a sale.
“I cannot discuss with the media about players that we want to buy," he added. "I cannot answer this question and not only about Strootman but all the players in this world."