The Cook Islands party is holding on to the resignation letter of its MP, Teina Bishop, and is yet to present it to the speaker of parliament to be formally recognised.
A CIP colleague, Wilkie Rasmussen, says Mr Bishop is planning to take the letter to the speaker if the party leader, Sir Geoffrey Henry, continues to refuse to do so.
Mr Rasmussen says the reason being given is that consultations with the constituency committee are needed but he believes the party is more concerned about the possibility of a by-election.
"To me, it would reflect perhaps weakness in the leadership, and in the Party structure, although the whole reason for Teina was more so the budget, but there has been some concern about the lack of coordination and I suppose support from the Party with regards to his issues."
Wilkie Rasmussen from the Cook Islands party.
An MP's resignation must be presented to the speaker of parliament before the seat can be declared vacant and a by-election held.