Van Gaal has been buoyed by the public support in recent days of Alex Ferguson, who called on United fans to be patient as the current manager awaits his first trophy with the club after almost two full seasons in charge.
Having been six points adrift of fourth-placed Manchester City in mid-February, United are now just one point behind going into the weekend's fixtures.
A 1-0 win at City two weeks ago was United's third victory in four league matches, and softened some of the disappointment that came with a Europa League exit at the hands of bitter rivals Liverpool.
"We are still capable of being in the top three in the league," he said. "We believe in it, and the players believe in that, which is much more important. We can win the FA Cup. We have a lot to fight for.
"We have five matches at home and three away, and that is also a benefit, I think. I hope that we show that in the next match. If you have to succeed a man like Ferguson, the expectations are very high.
United will be without midfielder Bastian Schweinsteiger for the Everton game, as he is likely to miss the rest of the season after tearing knee ligaments while training with Germany during the recent international break.
United captain Wayne Rooney is not ready to return against his former club, having been absent since mid-February with knee ligament damage. But the England striker has resumed light ball work in training and is likely to play for the club's Under-21 side soon -- either against Chelsea on Monday or Middlesbrough seven days later.
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