Yep, Kane might actually be one of the best candidates (outside of Lewandowski, Benzema and co.) when it comes to meeting the qualifiers for a Van Gaal type striker.
High work-rate is very underrated quality among strikers but of paramount importance under Louis. He will even prioritize a grafter who will work tirelessly within the constraints of the system than a finesse player who might be better overall in terms of productivity, but is lacking in the defensive side of the game (eg. Olic over Gomez even though the latter was a better forward at the time). And Kane really shines in this department. Not exactly Mandzukic levels yet, but Pocchettino's teams always player in a high-press system and he is always buzzing around in between the center-halves, or pressing further upfield, or dropping into deeper zones to maintain the integrity of Tottenham's defensive shape, and IIRC he won 30 tackles in the league last season - a very impressive number for a center forward. Such a refreshing attitude too. A lot of strikers have the propensity to get flustered when they're not scoring in a match, and they can essentially become liabilities the more frustrated they get. But Kane really evidenced the ability the work for his team-mates even when he wasn't necessarily having his best day goal-scoring wise.
This stat from Dec, 2014 illustrates his hard-working nature almost perfectly (and he didn't even score vs Swansea) :
Then he showed the ability to hold the ball up as a solitary striker in Tottenham's starting XI, a trait that will benefit any potential transition into United's probable 1-4-3-3 setup. Really strong as the focal point of attack (there were times last season when he shouldered all attacking responsibilities in the final third, especially when Eriksen went off the boil for a bit). In terms of physical presence and technical skill he resembles the prototypical Van Gaal striker too. Quite tall, decent speed, good range in terms of covering the ground, underrated technique, quality header of the ball, can shoot with either foot.
Now to be fair, he will never be a Drogba type powerhouse, but once he matures and piles on the muscles, he should be able to handle even the toughest opposition defenders the way a Van Persie could once he bulked up a bit, infact he fared really well against Terry last season. And Chelsea's defense under Mourinho is as hard as is gets. His variety in terms of goals scored is really impressive too. Outside the box, as a poacher, on the turn, off corners and set-pieces. Some of them aren't the most eye-catching in an aesthetic sense but that's because he generally seems to be in the right place at the right time, negating the need for wasted movement at the last second. And in terms of fundamental goal-scoring technique - he always aims to keep the shot down and wide from distance (scored a few of those last season too). A lot of his long-range efforts are with the ball touching the side-netting which indicates that he wants to put the ball as far away from the goalkeeper as possible to maximize the chance for scoring a goal.
Plus, you won't have to worry him getting into trouble off the field. Seems really grounded, and dedicated to the craft. That sort of attitude is always heartening to see, and suits a trainer coach like Van Gaal perfectly. Even if a player has flaws, Louis treats them as a pet project and is always open to the idea of sorting things out on the training field.
eg.
The biggest deficiency might be his limited sample size. Can he deliver over multiple seasons ? But that doesn't really matter that much under a proponent of youth like Louis anyway. Apart from that he checks out almost every box. Though of course Kane seems very content at Tottenham, and in terms of investment he might be a very risky proposition, given Levy's greedy nature. That's probably the only major downside.
. With Di Maria leaving we will be light on options for the right wing and striker. We would have Mata(a false winger- not van Gaal's ideal) and Januzaj (he's staying, but will have to improve dramatically) with the addition of Young and Memphis who are better on the left. Valencia is our new rightback and squad depth so not really a replacement. The only player who could potentially fill both gaps is Griezmann, given I haven't seen enough of him I can't judge him as a striker. He could play on the right wing though and could be available for a big bag of cash. The problem remains that van Gaal's ideal striker and ideal winger are different, I can only think of Muller who can play both positions to van Gaal's liking - but even then Muller is a better van Gaal 10.