Based on his philosophy and tactics, I think he could go with something like:
De Gea
Rafael - Smalling - Evans - ?
? - Carrick
Januzaj - Rooney - ?
Van Persie
Defenders
Based on what I've read previously, Van Gaal always likes a ball-playing defender, which is probably why we've been linked with Hummels lately, although I think Evans could do that job for us.
Midfielders
He seems to stress the importance of intelligence in midfield, mentioning the likes of Guardiola, Xavi and De Jong as 'thinkers', which is why I feel he'd love Carrick, as he reads the game tremendously. He just needs a dynamic player next to him who can piece things together for us.
Wingers
I also read in an article that he like's his wingers to stay wide and stretch play, therefore, I doubt we'd see Kagawa or Mata on the wings. At Bayern he went with Robben and Ribery on the wings who hugged the touchline, allowing the no.10 more room to work in. Therefore, I can see him going someone with wingers that will be always looking to beat their man with pace and trickery, such as Januzaj, Nani, Welbeck, Valencia. I do feel we need a winger in the Summer, though, hence the question mark in the line-up above. Probably a replacement for Nani.
This is what Van Gaal had to say about his wingers:
"For the left winger, for example, it is the space between the penalty area and the centre line on the corresponding side of the pitch."
http://thebusbybabe.sbnation.com/2014/4/26/5655302/louis-van-gaal-manchester-united-manager
Number 10
As for the number 10, from what he said, he wants them to be scoring 20-25 goals, making runs in behind the striker. He also has to be defensively good too, which is why I can see him opting for Wayne Rooney, as he's shown he can score goals from the CAM/SS position, and when he's on it, he'll get back and defend for the team. I can actually see him going with Welbeck in this position too.
He also mentions that he doesn't like his second striker to drop too deep, which will mean we'll need a ball playing midfielder to dictate play for us and be our link between midfield and attack. Similar players to Toure, Kroos, Fabregas, Schweinsteiger, etc. Time and time again, whether it be Rooney, Mata, Kagawa, or Welbeck playing behind the forward, due to our lack of invention and drive in midfield, at times, our CAM/SS have had to drop pretty deep. From what Van Gaal's saying, he likes them to stay behind the midfield line, where they can be a threat; either getting it to feet in a dangerous position, or running in behind.
Striker
Van Persie
From what he said, if he was to take over, i'd like to see something like:
De Gea
Rafael - Smalling - Evans - Shaw
Kroos - Carrick
Januzaj - Rooney - Reus
Van Persie