The Red Devils have already snapped up one defender this summer after the 20-time English champions completed a £27m deal for Southampton left-back Luke Shaw.
United have been heavily linked with a move for Germany’s World Cup-winning centre-half Hummels despite Borussia Dortmund insisting the 25-year-old is not for sale.
And Van Gaal, who penned a three-year deal with United in May, is hoping to replace Rio Ferdinand and Nemanja Vidic.
“We are doing well but we are looking for defenders. Defenders have gone and we have to replace them,” Van Gaal said.
Van Gaal praised Wilfried Zaha’s performance after the former Crystal Palace forward featured in a 0-0 draw with Inter Milan on Tuesday night.
“I was pleased,” Van Gaal added. “We have to wait and see. He has a lot of competition with the other strikers [for a first-team place].”
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