The source said the club have said they will make every effort to keep their captain, adding, though, that management is not despairing over Ramos' threat as they would have in years past.
The team captain is under contract through 2021 for more than €12 million per year after renewing in 2017. Spanish media, including El Chiringuito and Marca, both independently confirmed on Friday that Ramos is considering an exit and could move to another major European club.
Ramos has won 20 titles with Real Madrid in total including four European Cups, four Club World Cups, three UEFA Super Cups, four league titles, three Spanish Super Cups and two Copas del Rey.
According to the reports, both Manchester United and PSG have asked about Ramos' availability in the recent past, and the Madrid captain is considering a change as "something beneficial both for the team and on a personal level."
There was renewed optimism around Madrid when Zinedine Zidane -- who left after leading the club to three successive Champions League titles -- returned following a difficult season under first Julen Lopetegui and then Santiago Solari as managers in in the first seven months of the season. However, results have remained underwhelming.
A busy summer is expected as Zidane and club president Florentino Perez look to rebuild a side which won four of the five Champions League trophies from 2014 to 2018, but struggled last season and finished trophyless.
Eden Hazard, Paul Pogba, Luka Jovic, Ferland Mendy and Christian Eriksen are the names mentioned as potential summer arrivals, while there are big questions over the long-term futures of Gareth Bale, Keylor Navas, Isco, Luka Modric and Marcelo