I'm sure he will have checked if he can get Kane, that's just a given for me since he's English and fits the bill. If it wasn't for Levy I could see it happening, but I think Tottenham will hold onto him since he penned that contract. Never say never though, we might just have some spare funds somewhere we like to throw away.
Muller wouldn't even need to ask van Gaal if he's interested, but he's not leaving BM. No chance.
Lacazette I have only seen play 1 match of football, therefore I'm not really sure if he's suited for van Gaal playstyle. If he has potential to be an out-and-out striker I could see us going for him, but he can also play out wide so he could get more games (although we're stocked there so it wouldn't really help him). LvG his strikers usually aren't suited for a different role though so I just wouldn't know if Lacazette fits the bill.
Cavani, Higuain, Benteke seem like decent shouts. Not spectacular but proven quality players who can compete with Rooney if the latter is out of form. There aren't alot of strikers out there who look realistic and fit the bill van Gaal wants. Lewandowski would be the perfect van Gaal striker but I don't think he's available. I'm certain the Eredivisie doesn't have a striker we could be interested in so don't worry for random Dutch strikers.