Only elected councillors are elligible for the role and have until 4:30 p.m. today to register.
The person selected is likely to be from the same party as the city's former mayor, Gilles Vaillancourt.
The governing PRO-des-Lavallois party holds all but one seat on the city council.
Basile Angelopoulos, the vice-chair of the city's executive committee, has been at the helm of the city since Vaillancourt's resignation on Friday, following allegations of corruption.
Councillors Benoit Fradet and Jacques St-Jean have both confirmed they will not run.
Robert Bordeleau, head of the unelected opposition Service du Citoyen party, said he wishes it was possible to elect a candidate who is not a member of Vaillancourt's party.