The La Liga outfit made an official approach for the 40-year-old earlier this week after taking the decision to dismiss Jose Luis Mendilibar following a winless start to the new season.
However, they were instantly rebuffed, and went on to appoint former Almeria and Cadiz head coach Javi Gracia instead.
But, while Garcia has admitted to feeling flattered over the Spanish side's interest in him, he has reiterated his commitment to Brighton's cause.
"When a team from the first division in Spain, and who have been in that division for so many years, think of me to be their coach, it’s always a reason for pride," he told The Argus.
"But I’m sure of where I want to be and that is here. I’m happy to be here. Hopefully I’m here for many years.
"I’ve always wanted to coach in England and people have welcomed me. I think I can do a good job here and, all the time the club and the people here are happy with me, I’m happy here."
Garcia only took the Brighton job in June after the south-coast side elected to part ways with Gus Poyet.
The 40-year-old has since overseen a solid start to the new season, with Brighton having accrued seven points from their first five games.
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