Leweni played a major role in the country's 2006 coup and has been responsible for censoring local media, deporting Australian and New Zealand journalists and curbing free speech.
He, like others directly connected to the country's regime, is banned from even travelling to New Zealand or Australia.
But the Fiji government hopes to have him officially installed in a counselling post in Wellington under a new arrangement to boost diplomatic ties between the two countries.
New Zealand's foreign minister Murray McCully offered the extra posting earlier this month as an olive branch to mend regional relations and help return Fiji to democracy earlier than the 2014 election date set by leader Commodore Voreqe Bainimarama.
Nomination 'yet to be confirmed'
The self-appointed prime minister has broken several promises to go to the polls since staging a December 2006 coup.
Bainimarama's office told the Fiji Village website it had nominated Leweni for the job, while Leweni himself says his nomination is yet to be confirmed.
Fiji government sources confirmed to Fairfax New Zealand that Leweni's name had been put forward.
Bainimarama did not confirm the name on Auckland's Radio Tarana on Thursday but said he was awaiting New Zealand's response on the posting.
"We are extremely pleased that the New Zealand government is taking a step forward in redeeming our diplomatic relations," he told the station.
"We have submitted our nominee for the position for counsellor as agreed to in our initial meeting between our two foreign ministers.
"New Zealand is yet to respond on this."
--
Epi D
chief strategist
Solivakasama Worldwide Movement
www.solivakasama.org
