New Zealand's next governor-general could be the first All Black to fill the role – and possibly take up the post as the Rugby World Cup starts.

Sir Wilson Whineray, 76, is the pick among the Wellington establishment to take over from Sir Anand Satyanand, who ends his term in August.

Prime Minister John Key has hinted the next governor-general will not be a lawyer, saying whoever holds the post will get good constitutional advice.

Whineray was tipped for the job five years ago when Satyanand was appointed, with his experience as a judge and lawyer crucial.

Within Wellington circles, Whineray's frequent and often discreet service to the country is legendary. He is seen as a uniting figure at a time the country is suffering the trauma of the Christchurch earthquake. He has little political baggage and enjoys cross-party support.

No All Black has taken the top constitutional post, although two governors-general have lent their names to the game – the Earl of Ranfurly (1897-1904) and Lord Bledisloe (1930-35).

Appointing Whineray would also provide the opportunity of having the Rugby World Cup presented to the winning side by a legend of rugby. When New Zealand won in 1987, the trophy was presented to David Kirk by John Kendall-Carpenter, organising committee chairman.

The former prop captained the All Blacks in 30 tests between 1957 and 1965, and went on to study at Harvard and forge an outstanding business career, including a stint as chairman of Carter Holt Harvey.

Former Commonwealth Secretary-General Sir Don McKinnon, 72, whom Labour opposes, is another contender.

He was a National Party MP from 1978 to 2000 under both Rob Muldoon and Jim Bolger. He was foreign affairs minister between 1990 and 1999, resigning to take his Commonwealth role from 1999 to 2009.

Although a government can appoint anyone, convention requires multi-party consensus. There was uproar when former National Party PM Sir Keith Holyoake became governor-general in 1977, the only former politician in the role in modern times. He was 74 at the time and was appointed for three years rather than five.