The Samoa Observer newspaper reported the political party whip of the ruling Human Rights Protection Party, Alai'asā Sepulona Moananu, saying caucus members will vote for a new deputy leader before then.
The vote comes after the role was left vacant last week by the sudden resignation of the long-serving MP Fiame Naomi Mata'afa from the ruling party.
A likely candidate for the role is the long serving MP for Palauli le Falefa constituency, Faumuina Tiatia Liuga.
Faumuina, a previous contender for the deputy prime minister's post after the 2016 General Election, lost to Fiame by a 21-19 caucus vote.
Another former Deputy Prime Minister, Fonotoe Nuafesili Lauofo Meredith, is also seen as a possible contender for the role.
The vote is reportedly to be held during a caucus meeting this Friday.
The Prime Minister, Tuilaepa Sailele Malielegaoi, is also likely to assign the natural resources and environment portfolio, also vacated by Fiame, to his incoming deputy.
Meanwhile KHJ News reported next week's session of Parliament was also expected to deal with proposed amendments to the Electoral Act which were challenged in court for being discriminatory.