The 37-year-old won 112 caps for Australia in an illustrious career where he established himself as one of the world's best number 10s but he last played Super Rugby in 2007 and has been coaching the Brumbies' backs for the last two seasons.
"He runs all of our plays, he knows our plays - we would be crazy not to ask him, and it is a real option I could have Stephen Larkham running around for three games," South African White was quoted as saying in Thursday's Sydney Morning Herald.
"I would never force him to play, but when two fly-halves go down you have to think outside the box.
"If we think he can add value to us then we will pursue it ... he's 37 but there aren't many guys out there and the ones who are, they aren't much younger.
"If he says to me he would play, then of course we will go with that."
Lealiifano was ruled out for the season after he broke his ankle in last weekend's victory over the New South Wales Waratahs, which gave the Brumbies a nine-point lead at the top of the Australian Conference.
The Brumbies, who with Larkham won the Super Rugby title in 2001 and 2004, had already lost flyhalf Matt Toomua for the year to a knee injury that required surgery.