Botswana has emerged as the country that offered to sponsor Kevin Rudd's bid for the top job at the UN.

The African country's president, Ian Khama, called Prime Minister Malcolm Turnbull at the Lodge on August 13 to test the waters, News Corp Australia reported on Sunday.

But Mr Turnbull called him back to tell him the decision was "entirely a matter for you".

The report conflicts with Mr Turnbull's comments in New York last month that no country had raised with him the issue of Mr Rudd's nomination for the job.

The Turnbull government had earlier declined to endorse the former prime minister for the UN secretary-general post which went to former Portuguese prime minister Antonio Guterres.