Havelange quit as FIFA's honorary president last month, shortly before the publication of a report by the federation's ethics committee into allegations he took bribes from the ISL sports marketing company while president of football's governing body.
"The name Joao Havelange is today linked to fraud investigations and scandals at FIFA," said city councillor Renato Cinco, one of the proponents of the legislation.
"It doesn't make sense for a city which is going to host the World Cup and Olympic Games have the name of its stadium with this reference."
The stadium, often known as the Engenhao but officially named the Joao Havelange Olympic stadium, was built for the 2007 Panamerican games but was closed for repairs in March after structural problems were found in the roof.
It is due to be used for the athletics events when Rio hosts the 2016 Olympics, although the opening and closing ceremonies will be at the Maracana.
The councillors have suggested changing the stadium's name to Joao Saldanha, who coached Brazil in the 1970 World Cup qualifying competition.
"The change of name to Joao Saldanha is an attempt to resolve not just a matter of ethics, considering that Joao Havelange is not worthy of this tribute, but also to bring fresh air to this stadium built on the basis of overblown costs and with structural problems," said councillor Eliomar Coelho, another of the authors of the bill.
A Swiss prosecutor said in a legal document last July that Havelange and former FIFA executive committee member Ricardo Teixeira, took multi-million bribes from ISL on World Cup deals in the 1990s.
The FIFA ethics committee report also said that "not inconsiderable amounts" were channelled to Havelange and Teixeira from ISL, and there was no indication either of them gave any service in return.
Teixeira, formerly Havelange's son-in-law, was president of the Brazilian Football Confederation from 1989 until last year.
- Sports & Recreation
- Joao Havelange
- Joao Saldanha