MEXICO CITY, April 24 (Reuters) - Mexican lawmakers could vote as early as this week on a stock market reform bill, which aims to lure more companies to offer shares to the public, a source close to the process said on Monday.

The government, along with the country's two main stock exchanges, the Bolsa Mexicana de Valores (Grupo BMV) and the Bolsa Institucional de Valores (BIVA), put together the proposal.

Lawmakers in the Senate's treasury and public credit committee are slated to vote on the measure on Tuesday and then it would move to the Senate's plenary on Thursday, said the source, who has direct knowledge of the matter but asked not to be named.

Mexico has faced a stream of companies delisting and problems luring other firms to offer IPOs.

"We have a stock market in Mexico that isn't in its best moment in terms of company listings, but more importantly it's not of a size fitting of the Mexican economy," Marcos Martinez Gavica, BMV's chairman, said in a local radio interview.

"That's why we're so happy ... about this possibility of the new market law being approved which will make accessing the market easier, more efficient, cheaper, faster," said Martinez.

Maria Ariza, chief executive BIVA, told Reuters in March the reform would "boost and accelerate the entry of new entities to the market," particularly smaller firms.

A consensus among company executives and authorities has emerged that such a reform is needed, she said, highlighting that it will include simplified registration and allow a company to go public in just around three weeks.

Ariza argued more needs to be done to convince growing companies, including local unicorns - privately held startups valued at over $1 billion - to list shares on the local exchange rather than abroad. (Reporting by Anthony Esposito and Raul Cortes Fernandez; Editing by Muralikumar Anantharaman)