Hooper was selected for the Rugby Championship opener against Argentina in Mendoza last Saturday, August 6th, but flew home after informing coach Dave Rennie (58) he was not in the right frame of mind to play.
Veteran prop James Slipper (33) stood in as captain and led Australia to a 41-26 win.
White said Hooper had been in touch with team mates to offer congratulations from Australia but there was no indication when he might rejoin them.
"I spoke to him after the game once he touched down. Obviously, he was stoked with the result," White told reporters from the team hotel in Mendoza.
"And yeah, we'll stay in contact with him. Obviously, he's got a lot of support around him.
"He's not on his own now. So the staff put a good plan in place for him.
"I don't think there is (a timeline on his return)."
The injury-hit Wallabies meet the Pumas again in San Juan on Saturday, August 13th, before heading home to play world champions South Africa in Adelaide on August 27th.
The players thrilled Rennie and his staff with their brave performance in Mendoza as they shrugged off Hooper's late withdrawal and injuries to key players to overhaul the Pumas.
Starting hooker Dave Porecki (29) was ruled out due to concussion in the leadup to the test, while flyhalf Quade Cooper (34) joined Samu Kerevi (28) on the long-term injury list after suffering a serious Achilles injury midway through the match.
White said the Wallabies would need to be ready for a backlash from Michael Cheika's (55) Pumas, who gave up 19-10 lead at halftime in Mendoza and would be disappointed with their performance.
"Cheika will have them fired up," said White of the former Wallabies boss.
"The emotion will be there but we need to get back to the process of ... how we want to play, what our identity is.
"Plenty there for us to fix."
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