But talk of the 32-year-old extending his loan deal from Japanese outfit Suntory Sungoliath has been gathering pace ever since fellow openside David Pocock was ruled out of the Brisbane, Melbourne and Sydney showdowns with a torn ACL.
And while neither the Brumbies or the Australian Rugby Union are yet to confirm whether Smith would be available for longer than his initial 12-week secondment, White is hopeful that a deal will soon be reached.
"Don't forget they love the fact that Suntory get some mileage and Japanese rugby gets some mileage," White told Australian Associated Press.
"So I'm sure if we find a way in which we can keep him fresh and give him enough time to play and make sure he's 100 per cent ready for their season... I'm sure that they would look at accommodating us."
White believes Suntory's primary concern is to have their star signing fit and raring to go for the start of the Japanese season on August 18 so holding on to Smith for a little longer now seems a real possibility.
Under the terms of his current contract, Smith's last game for the Brumbies is due to be on May 31 when they face the Hurricanes.
That leaves the June 7 match with the Rebels and the July 13 clash against the Force as the only Super XV fixtures Smith is set to miss before the finals from July 19 to August 3.
And although it remains unclear whether Suntory would sanction Smith's availability for the Wallabies or if the ARU would back down on their decision not to field foreign-based players, an extension would at least see him feature in a mid-week fixture against the tourists even if he wasn't given permission for return to the Green and Gold 12 years after he last took on the Lions in the international arena.
White's side host the Lions on Tuesday, June 18 at Canberra Stadium in the sixth game of the upcoming tour in a game that doubles as the final warm up fixture prior to the opening Test four days later.