Napoli and Real Sociedad are among the clubs linked with a move for the 21-year-old winger.
Garnacho joined Chelsea last August after requesting a move away from Manchester United under Rúben Amorim. His debut season at Stamford Bridge produced eight goals across all competitions, with only one in the Premier League — a return that fell well short of expectations for a player signed as a wide attacking option to challenge the first-choice starters.
The arrival of Xabi Alonso as manager following Liam Rosenior's departure in April has accelerated the squad assessment. Alonso's preferred attacking structure is built around Cole Palmer, Estévao Willian and João Pedro, with Geovany Quenda arriving from Sporting CP this summer.
That leaves little room for Garnacho, who failed to establish himself as either a starter or a reliable impact substitute.
According to journalist Simon Phillips, Chelsea are seeking to recoup the full £40 million they paid United. The decision to sell at cost — rather than take a loss — reflects the belief that the summer market will generate sufficient interest to command that fee. Napoli have been linked with renewed interest having previously explored a move.
Any sale would generate funds for United under buy-back or sell-on clauses that depend on the structure of last summer's agreement, though the details of those arrangements have not been made public.
Garnacho will join Argentina's World Cup squad this week, offering him a platform to generate wider interest ahead of any summer negotiation.