The Galicians are aware of growing transfer interest in the Spanish international, with four league goals and five assists for him, in 37 La Liga games last season.
The club rejected a €10m bid for the 25-year-old last month, as per reports from Marca, with demands for a fee in the region of €15m needed to tempt them into a possible sale.
However, with Celta under no real pressure to sell, reports from La Voz de Galicia, via Diario AS, claim a breakthrough has now been reached with La Real.
The Basque giants have tabled a successful €15m offer in the last 24 hours with Celta now prepared to sell their midfield star.
Mendez will undergo a medical at the Estadio Anoeta this weekend with a transfer expected to be wrapped up in the coming days.