The former Barcelona and Arsenal player was named Brazil's Under-23 team coach for the 2020 Tokyo Olympics in April.
However, L’Equipe reported on Friday that the 45-year-old has already been released from his duties with the national team and will succeed Bruno Genesio in charge of the Ligue 1 side.
Genesio is set to leave Lyon at the end of the current campaign after three-and-a-half seasons at the helm and L'Equipe reported Sylvinho is certain to replace him after agreeing terms on Friday.
The Brazilian will be given a two-year contract, according to RMC Sport, after being chosen by his compatriot Juninho, who will take over as sporting director.
Sylvinho has never coached a club at senior level, but has had spells as an assistant with the Brazil national team, Inter Milan and Corinthians.
Lyon are third in Ligue 1 with two games of the season remaining.
(Reporting by Alasdair Mackenzie; Editing by Toby Davis)
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