The Red Devils boss wants to chase down their cross-town rivals after a solid start to the season and the 3-1 win over rivals Liverpool
A 3-1 victory over rivals Liverpool at Old Trafford on Saturday moved them into second place in the early-season table, with only their local rivals left in front of them.
Van Gaal has told the United squad they still have some improvements to make, but praised them for their performances and results in 2015-16.
"We have qualified [for the Uefa Champions League], we have 10 points out of five matches and I think that is a good record – there is only one club better," said the 64-year-old at his post-match press conference.
"Our aim is to be the best. Now we are five points behind Manchester City so we still look to that position, but I am happy.
"In a difficult period like we had in the transfer period with a lot of problems with players coming and going then I think we have managed it very well."
Van Gaal was impressed with the majority of the game against Liverpool, but wanted his team to show more of a killer instinct after Daley Blind's well-worked opening goal, with Ander Herrera's penalty and Anthony Martial's debut strike eventually getting the job done.
"I think the performance was good, we had very high control of the match until the first goal," the Dutchman said.
"It was a fantastic ‘studied’ goal so all the meetings and training sessions have paid off and it was also a wonderful shot from Daley.
"Still I want to improve. After that we didn’t kill the game and we have to do that but the first goal decided the match because they had to come at us, giving us more space so we could score more."
United travel to face PSV in their Champions League opener on Tuesday before facing another away game against Southampton in the Premier League on Sunday.