The Galician side have already been active in the market, agreeing a deal worth around âŹ9m to bring in goalkeeper Leo RomĂĄn from Real Mallorca as one of their first pieces of business, a fee made more accessible after Mallorca's own relegation to Segunda.
Sporting director Fernando Soriano has said the club expects to make seven or eight signings this summer as it builds a squad capable of surviving in the top flight, having made comparatively modest additions the previous season during the promotion push.
Attention has now turned to further additions across the squad. Chief among the names being discussed is Ălvaro Morata, the 33-year-old Spain international currently at Como, whose experience at the top level would offer an immediate boost to a newly promoted squad.
Deportivo are also said to be considering two players with greater long-term upside: Borussia Dortmund's 23-year-old forward FĂĄbio Silva and Grasshopper's 20-year-old Jonathan Asp Jensen.
The trio would sit alongside other areas Deportivo are working on, including the attacking department following Samuele Mulattieri's departure, where Uruguayan forward Fede Viñas has also emerged as an option after a reported âŹ4m proposal from the club.
The full-back positions are also under review, with Galician-born Angeliño of Roma previously floated as a possible reunion given his boyhood ties to the club, though Real Betis are also thought to be monitoring the left-back.
None of the moves appear close to completion at this stage, with Deportivo weighing up a squad that blends experience with promising younger talent as they prepare for life back among Spain's elite.
The summer window remains open until 1 September, giving the club time to work through its list of targets without being forced into hasty decisions.