The Holland boss is keen to get the players future sorted and for him to be settled ahead of their World Cup Qualifier campaign, but has said that only the player can decide where his future lies.
Van Gaal spoke at a press conference and said: "I think the player always has to decide for himself.
"When he wants he can ask me for advice but then I'll speak to him, not to you."
He added: "I had the conversation and it was unbelievable. A great and high level, not only at a human side but also in the football vision. It was one of the best meetings I've had with an individual player."
When he was quizzed over whether it was important, with next month's qualifiers approaching (Turkey & Hungary), that Van Persie decided his future sooner rather than later, the former Ajax and Bayern Munich boss added: "Yes, of course. But it's for the English clubs, and Arsenal of course, to decide."