Mr Birmingham told Today the Federal Government is offering consular support to Cheng and her family.
“We are doing everything we can in providing her and her family with assistance through what is no doubt a difficult time for them.
Mr Birmingham confirmed the Federal Government had been formally told by authorities on August 14 of her detention.
But they had not said why the television anchor with Chinese state-run channel CGTN was being held.
“But we will continue to work to ensure that the right assistance is provided to give her and her family every support,” Mr Birmingham said.
Australian consular officials spoke with Cheng at the detention facility via a video link last Thursday.
But Mr Birmingham said Australia’s values “are not for sale”.
“Our government has been very clear that our values are not for sale. We will always defend our interests and Australia’s security interests in particular.”
He said Australia wanted a “constructive relationship” with China.
“We have different systems of government. We bring different approaches to those systems of government but we respect their sovereignty and we simply ask for that to be reciprocated.”
Cheng has not been charged with any crime but is under “residential surveillance at a designated location” in Beijing, the ABC reports.
Residential surveillance is detention without legal access and can last up to six months before a suspect is formally arrested or charged.
Cheng studied at Queensland University and began her career in finance in Australia, where she worked for corporations including Cadbury.
She is a high-profile anchor of the Global Business show on the English-language channel of the China Global Television Network, a state-run media organisation.
“As a family we are aware of the current situation with regard to Cheng Lei’s status as advised by the Department of Foreign Affairs and Trade (DFAT),” the statement said.
“We are in close consultation with DFAT and doing everything we can as a family to support Cheng Lei.
“In China, due process will be observed and we look forward to a satisfactory and timely conclusion to the matter.
“We ask that you respect that process and understand there will be no further comment at this time.”
Cheng has been with CGTN since 2012 and has reported on Asian affairs in China since 2002.
She has reported major Chinese events including Beijing’s 2008 Olympics and Shanghai’s 2010 World Expo.