The federal government says it will announce the next governor-general “in due course”, but insists a decision has not been made.

The federal government insists a decision has not been made on who the next governor-general of Australia will be, despite reports saying former general Peter Cosgrove has been picked.

A spokeswoman for Prime Minister Tony Abbott’s office told AAP on Thursday “no decision has been made yet”.

“An announcement will be made in due course as per the usual process,” she said.

Mr Cosgrove, a popular former chief of the defence force, has been considered a frontrunner to replace Governor-General Quentin Bryce and serve a five-year term from March.

Acting Prime Minister Warren Truss said Mr Cosgrove would be an excellent candidate, but there were other suitable candidates.

“I just don’t want to speculate on who might fill the position,” Mr Truss told reporters.

However, News Corp Australia reported on Thursday that a decision had been taken.

Australian Monarchist League chairman Philip Benwell said speculation about the appointment of “Her Majesty’s representative in this country” was highly inappropriate.

“The office of governor-general is not a political office nor is it a popularity contest and, above all, it should never be the subject of media speculation,” he said in a statement.

The league said it was particularly incorrect to speculate before the Queen had received formal advice from the prime minister.

Mr Cosgrove led the Australian contingency in the 1999 East Timor peacekeeping mission, subsequently commanding the army and serving as defence force chief from 2002 to 2005.

Since leaving the military he has worked as a non-executive director of Qantas, a Deloitte Touche Tohmatsu consultant and been the chairman of the South Australian Defence Industry Development Board and peak aged services industry body Leading Age Services Australia.

Mr Cosgrove is the chancellor of the Australian Catholic University and until last year was the chairman of the Australian War Memorial Council.

A Townsville suburb was named after him in 2008 in recognition of his work leading the rebuilding task force after Cyclone Larry devastated northern Queensland.