The Red Devils have been heavily linked with bids for the pair in recent weeks, with newspaper reports suggesting on Friday that a £45 million bid for Tottenham striker Kane was being prepared ahead of the summer transfer window.
Goal understands that Tottenham will resist any offers for Kane, while Bale is determined to make a success of his move to Real Madrid, despite his recent downturn in form.
United are understood to have prioritised a move for the Welshman, however, though Van Gaal moved to quell any speculation in his pre-match press conference ahead of this weekend's clash with Arsenal.
When asked about moves for the duo, Van Gaal said: "You can mention a lot of names, I've seen that I buy everyone in the world but it's not like that."
Van Gaal did, however, hint at transfer activity this summer, as he seeks to "balance" his squad following a season disrupted by injuries to several key players.
Wayne Rooney and Luke Shaw have both been ruled out of Sunday's fixture, and Van Gaal has grown frustrated with the fitness problems plaguing his squad, though he admits transfers are often protracted.
"It's also dependable on how we can make a balance in our selection, I have said the most important thing is to make a balance in our selection because it is not good that I have to change positions of players because there are players injured," he added.
"We have to bring that balance back in the selection and that was not this year. Transfers is also a process. It's not 'okay, I want you' and he comes. There are always three parties; the player, the club and ourselves so it is not so easy."