The semi-public Brazilian multinational already sponsors Williams, but the team's engine deal with Mercedes means it actually uses Petronas lubricants and fuel.
Brazil's UOL reports that Petrobras executives therefore met recently with representatives of Renault and Toro Rosso.
Toro Rosso, the second Red Bull team, is set to switch from Ferrari to Renault power for 2016.
Red Bull is also powered by Renault, but the team is sponsored by Total, a French oil company. Toro Rosso was sponsored by the Spanish oil brand Cepsa until this year, but had to use Shell products for its current Ferrari engine deal.
UOL said Petrobras is keen to add a second team to its F1 roster so that it can actually develop and supply its products at the pinnacle of motor sport.
"It is crucial that there is an agreement with (engine supplier) Renault before discussing the details with Toro Rosso," read the media report.
The report added that Petrobras has significant work to do to prepare fuels and lubricants to the standards necessary for F1, having not done so since 2008.
"The tentative agreement with Toro Rosso does not signal the end of the partnership with Williams," UOL declared. "On the contrary, Petrobras is seeking the renewal of the contract that expires at the end of 2016."
The report said Toro Rosso's Petrobras link ties in with the test debut at Silverstone this week of Brazilian teen Sergio Sette Camara, who is sponsored by the company and also a member of the Red Bull junior team.