White has been impressed by Folau's transition to the 15-man code but insists he should make a long-term commitment to the sport to warrant Test selection.
"The concern is if you've only played 10 games and become a Wallaby, for me it's a bit of an indictment on the jumper," said White.
"I understand he's a great catch and they want to try and attract him marketing wise to keep him in rugby football. They [Australian Rugby Union] officials did the same with Mat Rogers, Wendall Sailor and Lote Tuqiri, and I understand that with the competition for codes here.
"But he's got to want to play for the Wallabies and be a part of the Wallabies for many, many years if you want to give him a Wallaby jumper.
"I don't think it would be fair after 10 or 12 games if he ends up playing for Australia. As I said it's a bit of an indictment for Australia."
Australia head coach Robbie Deans played down speculation this week but admitted Folau could become a legend of the game.
One player White insists should pull on the Gold and Green in the summer is Brumbies full-back Jesse Mogg.
The 23-year-old, who impressed in last season's Super Rugby campaign, has been a revelation this year and White draws comparison with Wallaby greats.
"He will play for Australia, I just don't want to rush him too quickly," added White.
"At the end of the day it's not about how you play for Australia, it's how many times you play for Australia. If you compare him to the likes of Joe Roff and Chris Latham, which is a massive honour for him, he's got to play 50 or 60 times for Australia not just be a one-hit wonder."