The Red Devils limped out of the Europa League on Thursday night after a 3-1 aggregate defeat by Jurgen Klopp’s Liverpool side.
The 20-time English champions could finish the season without silverware unless United beat West Ham in their FA Cup quarter-final replay next month.
Van Gaal’s position at Old Trafford has been under scrutiny in recent months amid reports Jose Mourinho or Ryan Giggs could replace the former Barcelona manager.
Speaking to ITV Sport, Keane offered Van Gaal some advice over potential signings in the summer if the Dutchman is still in charge.
“I know they’ve had injuries. It shows how important a fit Wayne Rooney is to this club. I’m looking for characters,” Keane told ITV Sport.
“Where are the leaders in this group?”
Keane added: “The pressure will be building. LvG is an experienced manager and he knows that. You hope he gets to the summer and he gets the opportunity to bring in quality players with a bit of character.”
United are in sixth place in the Premier League table and four points behind fourth-placed Manchester City.
The Red Devils drew 1-1 with the Hammers in their FA Cup quarter-final at Old Trafford last weekend.
United make the short trip to Manchester City on Sunday.
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