A board meeting on the nomination will be held on Friday, the paper added.
The bank was not immediately available for a Reuters request for comment. Le Figaro reported the bank declined to comment on the matter.
Krupa currently acts as deputy CEO in charge of Global Customers and Investor Solutions. He was seen as one of the frontrunners for the job.
According to several sources, Krupa is the "big favourite" to succeed to Frederic Oudea, who decided to leave the bank earlier this year, the report said.
"His candidacy has been preferred to that of Sebastien Proto ... by the nomination committee", the report said, referring to another internal candidate who had been cited as well placed for the job in the run-up to the nomination.
(Reporting by Tassilo Hummel, Editing by Dominique Vidalon)
