Justice Minister Michael Keenan has released a statement saying "a matter is under consideration by appropriate authorities".
He said no further comment will be made until "that process is complete".
Fairfax Media is reporting that unnamed sources claim that Mr Quaedvlieg's leave is related to personal behaviour.
Former Immigration Department spokesman Sandi Logan posted on a message on Twitter on Monday saying Mr Quaedvlieg had been "suspended" and was "under external investigation".
The former federal police officer became comissioner of the Australia Border Force in 2015.
He had been tasked with enforcing the Turnbull government's hardline policies on border protection.
He was formerly a member of the Queensland police force before he joined the Australian Federal Police in 2005, where he was the Chief Police Officer of ACT Policing.
