White is currently only eight months into a four-year deal with the Brumbies but is among the front-runners to take charge of England.
Brumbies chief executive Andrew Fagan is disappointed with the disruption the speculation has caused.
"Obviously this is a terrific opportunity for Jake White, and one which reflects his status as one of the world's leading coaches," Fagan said.
"It also speaks volumes about the quality of the rugby programme that Jake is putting in place here at the Brumbies that he should be sounded out for this role. That said, Jake is in the first of a four-year contract with the Brumbies, and there are many details that would need to be worked through should he be successful with his application."