Matangi Tonga reported it could take up to four weeks to complete the process of nominations and voting by the 25 sitting members.
Mr Pohiva passed away in Auckland last week and his state funeral will be held this Thursday in Nuku'alofa.
His body is being repatriated on a Royal New Zealand Airforce plane this afternoon.
The Prime Minister had not attended parliament this parliamentary session.
The House had been struggling to continue with its 2019 session because some of MPs were unable to attend either because of ill health or overseas travel.
It finally got started on 12 August, although there was a delayed start because they did not have a quorum.
Parliament must have a quorum of 13 before it can proceed.