United built an eight-point gap to fifth-placed Liverpool - 4-1 losers at Arsenal - courtesy of a fifth Premier League win in a row, with Ander Herrera scoring twice and Wayne Rooney netting a stunning goal at Old Trafford.
Van Gaal acknowledged afterwards that things are looking bright as far as qualification for Europe goes, and the Dutchman even hinted at very faint hopes of a title challenge.
He said: "We have to play still against the first three in the league, so it's [the top four] not done yet, but of course we have made a big gap so we can suffer a defeat.
"But I'm looking also higher up and then we have to win every week and then everything is possible.
"It is not likely that we shall be the champions, but when you give pressure - Arsenal is also giving pressure to Chelsea - it is possible. You never know. But normally Chelsea shall be the champions."
The United boss was relieved that the two-week break from league action for international fixtures failed to halt his side's momentum, with Christian Benteke's goal the only moment of worry in an otherwise commanding display.
"Before this match I was afraid because there was an international break between," he added. "We are in a good shape. The confidence has risen and then you play against a very defensive organisation. That is not easy.
"It is always a difficult match to win against a side battling relegation. We have created four or five chances and didn't give any chances away in the first half.
"We scored the first goal at the right time at the end of the first half. The first half was a good performance, but we have to finish more. The second half was more controlling."
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