The Premier League leaders have extended the proposal to the South American firm with a view to renaming the west London stadium Petrobas Stamford Bridge.
However, Brazilian magazine Veja reports that the business opportunity will be rejected by the company.
Proposal: Stamford Bridge
Petrobras is also said to have been approached by Manchester United before the club signed a shirt sponsorship deal with American insurers AON to replace AIG.
Real Madrid is also understood to have considered approaching the company as a possible partner.
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