Bordenave, 66, has been BNP Paribas' COO since 2011. His mandate as COO was extended last year for a further year.
Laborde is currently deputy COO in charge of retail domestic markets while Gerardin is deputy COO in charge of corporate and investment banking.
No decision had been formally taken, Les Echos said.
A BNP Paribas spokeswoman declined to comment.
(Reporting by Matthieu Protard; editing by David Evans)