The sale of the submarine cable business would be followed by other corporate operations around Telxius, the newspaper reported.
Telxius will operate 100,000 kilometres of submarine cable globally by 2021, according to its website.
A Telefonica spokesman declined to comment. Neither Societe Generale nor Greenhill were immediately available for comment.
Telefonica has been looking for ways to lighten its debt burden. Chief Operating Officer Angel Vila said last month that Telxius would "contemplate all possible alternative strategies for its underwater-cable unit".
(Reporting by Inti Landauro and Isla Binnie; Editing by Kirsten Donovan)