Despite the Blues’ preference to keep the World Cup winner, the Londoner team has placed a £120 million valuation on the midfielder as interest begins to build.
Fernandez, who joined from Benfica in January 2023 for a then-record fee, is said to be unsettled in London and is exploring new options ahead of the next transfer window.
His agent has already made contact with Real Madrid, with the Spanish giants emerging as a potential destination.
The 25-year-old vice-captain appeared to wave goodbye to supporters after Chelsea’s final game of the season, a defeat to Sunderland, further fuelling speculation over his future.
Chelsea are keen to resolve the situation quickly to bring stability to incoming head coach Xabi Alonso following a chaotic season of managerial changes.
Even at the uncertainty, Fernandez remains one of Europe’s most decorated midfielders, boasting World Cup and Copa America success with Argentina.