Imanol Alguacil has been in temporary charge of first-team affairs at the Anoeta since March after the departure of Eusebio Sacristan and has guided them to 10th place in the Spanish top-flight standings with one game to go.
However, the 46-year-old has a contract only until the end of the campaign and Real will then look to appoint a permanent boss.
Former Sociedad goalkeeper Roberto Olabe was appointed as the club’s director of sport in March and is the man charged with the task of identifying the next coach, with Gracia said to be on his list of possibilities, according to Marca.
Former Paris Saint-Germain boss Unai Emery and Leganes coach Asier Garitano are the other two names mentioned in the report, with the latter thought to be the club’s preferred choice.
However, it is said that Gracia ‘welcomed the proposal’ despite signing an 18-month deal with the Hornets when replacing of Marco Silva at Vicarage Road in January.
Bayer Leverkusen have signed keeper Lukas Hradecky from Eintracht Frankfurt ahead of Bernd Leno's likely exit.