Their absence at the August 5 ceremony highlights the political crisis in Brazil, with Rousseff facing possible removal from office in an impeachment trial shortly after the Games end. Lula, who as president was instrumental in Rio's winning bid as Olympic host, faces serious corruption allegations.
"She will not go," said a source from Rousseff's office at the Alvorada Palace residency in the capital Brasilia.
"Lula will not go," echoed Jose Chrispiniano, a spokesman at the Lula Institute in Sao Paulo.
The leftist leader says the impeachment process is a coup in disguise mounted by her former vice president, Michel Temer, who has been acting president ever since Rousseff's suspension in May. If she is removed permanently Temer would retain the presidency until 2018.
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Temer is expected to preside over the Games as Brazil's leader.
On Monday, Rousseff said in an interview with French radio RFI that she would refuse to attend the opening ceremony with anything less than presidential status.
Estadao newspaper recently reported that the invitation to Rousseff is similar to that sent out to several ex-presidents of Brazil, including her predecessor Lula, Fernando Henrique Cardoso, Fernando Collor de Mello and Jose Sarney.
Lula, who founded the Workers' Party and eased Rousseff to power after serving two presidential terms himself, was a key player in Rio's successful 2009 bid to stage the Games, the first ever in South America.
While Rousseff faces ejection from office, Lula is also struggling against serious corruption allegations related to the vast embezzlement conspiracy at state oil company Petrobras.